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[]
[null,"ROMBERG QUADRATURE",null,null,null,"CLICK THE ORANGE BUTTON"]
[null,"AND FUNCTION PLOTTING CHART",null,null,null,"CLICK BUTTON TO SWITCH",null,"SHOW /HIDE"]
[null,"Finite Interval (a,b)",null,null,null," BETWEEN \"SHOW RESULTS\" AND"]
[null,null,null,null,null," \"HIDE RESULTS\"",null,0]
[null,"UDF Name:   QUAD_ROMBERG_GD"]
[]
["FUNCTION PLOTTER",null,null,null,null,null,null,null,null,"OVERALL PROGRAM PERFORMANCE"]
["CLICK THE \"CLICK TO SHOW CHART\" BUTTON, THEN SELECT FUNCTION WITH UP/DOWN BUTTONS",null,null,null,null,null,"SELECT FUNCTION","SHOW / HIDE",null,"Total","Total Time","Total True","Total Number of"]
["No.","Cell Function Plotted","Name","Variable","a","b",null,null,null,"Func Evals:","in Seconds:","Error:","Correct Digits:"]
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[null,null,null,null,null,null,null,null,null,"↓↓↓","↓↓↓","↓↓↓","↓↓↓"]
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[null,"ROMBERG PROGRAM INPUTS",null,null,null,null,true,"ROMBERG PROGRAM OUTPUTS"]
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[37,"x/SQRT(1-x^2)","FINITE_37","x",0,1,{"$f":"1","v":1},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B52,D52,E52,F52),\"\")","v":""},"","","","","",""]
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[41,"1/(1+x^2+x^4+x^6)","FINITE_41","x",-1,1,{"$f":"PI()/4+LN(1+SQRT(2))/SQRT(2)","v":1.4086234035376788},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B56,D56,E56,F56),\"\")","v":""},"","","","","",""]
[42,"(PI()/4-x*TAN(x))*TAN(x)","FINITE_42","x",0,{"$f":"PI()/4","v":0.78539816339744828},{"$f":"LN(2)/2+PI()^2/32-PI()/4+(PI()*LN(2))/8","v":0.14179882570451702},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B57,D57,E57,F57),\"\")","v":""},"","","","","",""]
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[48,"x^2/(1+x^4)/SQRT(1-x^4)","FINITE_48","x",0,1,{"$f":"PI()/8","v":0.39269908169872414},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B63,D63,E63,F63),\"\")","v":""},"","","","","",""]
[49,"EXP(-(x^2))*LN(x)","FINITE_49","x",17,42,{"$f":"2.56572850056105E-127","v":2.5657285005610501E-127},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B64,D64,E64,F64),\"\")","v":""},"","","","","",""]
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[63,"SQRT(50)*EXP(-50*PI()*x^2)","FINITE_63","x",0,1,0.5,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B78,D78,E78,F78),\"\")","v":""},"","","","","",""]
[64,"50/(PI()*(1+2500*x^2))","FINITE_64","x",0,10,0.499363381076456,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B79,D79,E79,F79),\"\")","v":""},"","","","","",""]
[65,"x*SQRT(x)","FINITE_65","x",0,1,0.4,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B80,D80,E80,F80),\"\")","v":""},"","","","","",""]
[66,"x^0.5","FINITE_66","x",0,1,{"$f":"2/3","v":0.66666666666666663},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B81,D81,E81,F81),\"\")","v":""},"","","",{"$f":"IF($H$5=1,IF(AND(ISNUMBER(G81),ISNUMBER(H81)),IF(G81=0,ABS(ABS(G81)-ABS(H81)), ABS(ABS(G81)-ABS(H81))/ABS(G81)),\"\"),\"\")","v":""},{"$f":"IF($H$5=1,IF(AND(ISNUMBER(G81),ISNUMBER(H81)),IF(L81=0,15,IF(L81>1,0,IF(INT(ABS(LOG(L81)))>15,15,INT(ABS(LOG(L81)))))),\"\"),\"\")","v":""},{"$f":"IF($H$5=1,IF(OR(ISNUMBER(H81)=FALSE,M81=0),\"Cannot calculate\",\"\"),\"\")","v":""}]
[67,"COS(COS(x)+3*SIN(x)+2*COS(2*x)+3*SIN(2*x)+3*COS(3*x))","FINITE_67","x",0,{"$f":"PI()","v":3.1415926535897931},0.83867634269442903,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B82,D82,E82,F82),\"\")","v":""},"","","","","",""]
[68,"EXP(-x/5)*(2+SIN(2*x))","FINITE_68","x",0,10,{"$f":"9.108239607323","v":9.1082396073230001},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B83,D83,E83,F83),\"\")","v":""},"","","","","",""]
[69,"x^(-1/3)*(1-x)^5","FINITE_69","x",0,1,{"$f":"2187/5236","v":0.41768525592055006},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B84,D84,E84,F84),\"\")","v":""},"","","","","",""]
[70,"SIN(PI()*x)","FINITE_70","x",0,1,{"$f":"2/PI()","v":0.63661977236758138},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B85,D85,E85,F85),\"\")","v":""},"","","","","",""]
[71,"x^0.25","FINITE_71","x",0,1,0.8,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B86,D86,E86,F86),\"\")","v":""},"","","","","",""]
[72,"x*SIN(20*x)*COS(50*x)","FINITE_72","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"2*PI()/105","v":5.9839860068377014E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B87,D87,E87,F87),\"\")","v":""},"","","","","",""]
[73,"LN(1/x)*x^4","FINITE_73","x",0,1,0.04,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B88,D88,E88,F88),\"\")","v":""},"","","","","",""]
[74,"COS(8*SIN(x)-x)","FINITE_74","x",0,{"$f":"PI()","v":3.1415926535897931},{"$f":"PI()*0.234636347","v":0.73713182400034549},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B89,D89,E89,F89),\"\")","v":""},"","","","","",""]
[75,"x*COS(x)*SIN(30*x)","FINITE_75","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"-60*PI()/899","v":-0.20967247966116526},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B90,D90,E90,F90),\"\")","v":""},"","","","","",""]
[76,"x*COS(50*x)*SIN(30*x)","FINITE_76","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"60*PI()/1600","v":0.11780972450961723},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B91,D91,E91,F91),\"\")","v":""},"","","","","",""]
[77,"LN(x)*LN(1-x)","FINITE_77","x",0,1,{"$f":"2-PI()^2/6","v":0.35506593315177359},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B92,D92,E92,F92),\"\")","v":""},"","","","","",""]
[78,"SIN(2*x)^2","FINITE_78","x",0,{"$f":"PI()","v":3.1415926535897931},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B93,D93,E93,F93),\"\")","v":""},"","","","","",""]
[79,"x^(5/6)*(4-x)^(1/6)/(5-x)/(6-x)/(7-x)","FINITE_79","x",0,4,{"$f":"(4*3^(5/6)-5^(5/6)-3^(1/6)*7^(5/6))*PI()","v":0.28420541078666034},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B94,D94,E94,F94),\"\")","v":""},"","","","","",""]
[80,"1/(1+TAN(x)^3)","FINITE_80","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()/4","v":0.78539816339744828},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B95,D95,E95,F95),\"\")","v":""},"","","","","",""]
[81,"ATAN(SQRT(x^2+1))/SQRT(x^2+1)/(x^2+1)","FINITE_81","x",0,1,{"$f":"PI()/4-PI()/2*SQRT(2)+3/2*SQRT(2)*ATAN(SQRT(2))","v":0.59048927088638559},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B96,D96,E96,F96),\"\")","v":""},"","","","","",""]
[82,"LN(1-4*COS(x)+4)","FINITE_82","x",0,{"$f":"PI()","v":3.1415926535897931},{"$f":"2*PI()*LN(2)","v":4.3551721806072043},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B97,D97,E97,F97),\"\")","v":""},"","","","","",""]
[83,"1/(1+COS(x)^x)","FINITE_83","x",{"$f":"-PI()/2","v":-1.5707963267948966},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B98,D98,E98,F98),\"\")","v":""},"","","","","",""]
[84,"1/SQRT(ABS(x-1))","FINITE_84","x",0,1,2,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B99,D99,E99,F99),\"\")","v":""},"","","","","",""]
[85,"1/SQRT(x)*LN(1/x)","FINITE_85","x",0,1,4,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B100,D100,E100,F100),\"\")","v":""},"","","","","",""]
[86,"1/x^(1/4)*LN(1/x)","FINITE_86","x",0,1,{"$f":"16/9","v":1.7777777777777777},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B101,D101,E101,F101),\"\")","v":""},"","","","","",""]
[87,"SIN(x)/x","FINITE_87","x",0,1,0.94608307036718298,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B102,D102,E102,F102),\"\")","v":""},"","","","","",""]
[88,"SIN(x)^2*COS(x)^4","FINITE_88","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"PI()/8","v":0.39269908169872414},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B103,D103,E103,F103),\"\")","v":""},"","","","","",""]
[89,"LOG(1+TAN(x))","FINITE_89","x",0,{"$f":"PI()/4","v":0.78539816339744828},{"$f":"PI()*LOG(2)/8","v":0.11821420286101633},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B104,D104,E104,F104),\"\")","v":""},"","","","","",{"$f":"IF($H$5=1,IF(OR(ISNUMBER(H104)=FALSE,M104=0),\"Cannot calculate\",\"\"),\"\")","v":""}]
[90,"SIN(SIN(x))","FINITE_90","x",0,1,{"$f":"0.430606103120691","v":0.43060610312069098},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B105,D105,E105,F105),\"\")","v":""},"","","","","",""]
[91,"x*COS(x^2+1)","FINITE_91","x",0,2,{"$f":"(SIN(5)-SIN(1))/2","v":-0.90019762973551742},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B106,D106,E106,F106),\"\")","v":""},"","","","","",""]
[92,"x^2*(x^2-2)*SIN(x)","FINITE_92","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()^3/2-14*PI()+28","v":-0.47915881010719374},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B107,D107,E107,F107),\"\")","v":""},"","","","","",""]
[93,"x^3/(EXP(x)-1)","FINITE_93","x",0,15,{"$f":"PI()^4/15","v":6.4939394022668289},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B108,D108,E108,F108),\"\")","v":""},"","","","","",""]
[94,"LN(x)/(1+x)","FINITE_94","x",0,1,{"$f":"-(PI()^2/12)","v":-0.8224670334241132},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B109,D109,E109,F109),\"\")","v":""},"","","","","",""]
[95,"SQRT(1-0.5*SIN(x)^2)","FINITE_95","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"1.35064388104768","v":1.35064388104768},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B110,D110,E110,F110),\"\")","v":""},"","","","","",""]
[96,"LN(x)^3","FINITE_96","x",0,1,{"$f":"-6","v":-6},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B111,D111,E111,F111),\"\")","v":""},"","","","","",""]
[97,"1/(PI()*SQRT(1-x^2))","FINITE_97","x",-1,0.5,0.66666666666666596,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B112,D112,E112,F112),\"\")","v":""},"","","","","",""]
[98,"LN((1+x)/(1-x))/4/LN(2)","FINITE_98","x",-1,0.5,{"$f":"((1+0.5)*LN(1+0.5)+(1-0.5)*LN(1-0.5))/4/LN(2)-0.5","v":-0.40563906222956642},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B113,D113,E113,F113),\"\")","v":""},"","","","","",""]
[99,"(23/25*COSH(x)-COS(x))","FINITE_99","x",-1,1,{"$f":"46/25*SINH(1)-2*SIN(1)","v":0.47942822668880147},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B114,D114,E114,F114),\"\")","v":""},"","","","","",""]
[100,"2/(2+SIN(10*PI()*x))","FINITE_100","x",0,1,{"$f":"2/SQRT(3)","v":1.1547005383792517},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B115,D115,E115,F115),\"\")","v":""},"","","","","",""]
[101,"SIN(100*PI()*x)/PI()/x","FINITE_101","x",0,1,{"$f":"0.498986808693045","v":0.49898680869304501},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B116,D116,E116,F116),\"\")","v":""},"","","",{"$f":"IF($H$5=1,IF(AND(ISNUMBER(G116),ISNUMBER(H116)),IF(G116=0,ABS(ABS(G116)-ABS(H116)), ABS(ABS(G116)-ABS(H116))/ABS(G116)),\"\"),\"\")","v":""},{"$f":"IF($H$5=1,IF(AND(ISNUMBER(G116),ISNUMBER(H116)),IF(L116=0,15,IF(L116>1,0,IF(INT(ABS(LOG(L116)))>15,15,INT(ABS(LOG(L116)))))),\"\"),\"\")","v":""},{"$f":"IF($H$5=1,IF(OR(ISNUMBER(H116)=FALSE,M116=0),\"Cannot calculate\",\"\"),\"\")","v":""}]
[102,"1/(1+COS(x))","FINITE_102","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"1","v":1},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B117,D117,E117,F117),\"\")","v":""},"","","","","",""]
[103,"1/(1.005+x^2)","FINITE_103","x",-1,1,{"$f":"1.56439644406904","v":1.5643964440690401},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B118,D118,E118,F118),\"\")","v":""},"","","","","",""]
[104,"4*PI()^2*x*SIN(20*PI()*x)*COS(2*PI()*x)","FINITE_104","x",0,1,{"$f":"-20*PI()/99","v":-0.63466518254339255},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B119,D119,E119,F119),\"\")","v":""},"","","","","",""]
[105,"1/(1+(230*x-30)^2)","FINITE_105","x",0,1,{"$f":"0.0134924856494677","v":1.34924856494677E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B120,D120,E120,F120),\"\")","v":""},"","","","","",""]
[106,"50*(SIN(50*PI()*x)/(50*PI()*x))^2","FINITE_106","x",0,1,{"$f":"0.498986808693045","v":0.49898680869304501},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B121,D121,E121,F121),\"\")","v":""},"","","","","",""]
[107,"COS(COS(x)+3*SIN(x)+2*COS(2*x)+3*COS(3*x))","FINITE_107","x",0,{"$f":"PI()","v":3.1415926535897931},0.29101878286005201,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B122,D122,E122,F122),\"\")","v":""},"","","","","",""]
[108,"x^63","FINITE_108","x",0,1,{"$f":"1/64","v":1.5625E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B123,D123,E123,F123),\"\")","v":""},"","","","","",""]
[109,"1/(x+0.5)","FINITE_109","x",0,1,{"$f":"LN(3)","v":1.0986122886681098},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B124,D124,E124,F124),\"\")","v":""},"","","","","",""]
[110,"SQRT(12.25-(5*x-3)^2)","FINITE_110","x",0,1,{"$f":"(SQRT(132)+SQRT(117)+49/2*(ASIN(6/7)+ASIN(4/7)))/20","v":3.1217683711646531},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B125,D125,E125,F125),\"\")","v":""},"","","","","",""]
[111,"10/(1+(10*x-4)^2)","FINITE_111","x",0,1,{"$f":"PI()-ATAN(10/23)","v":2.731465313048302},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B126,D126,E126,F126),\"\")","v":""},"","","","","",""]
[112,"1/SQRT(x*(1-x))","FINITE_112","x",0,1,{"$f":"PI()","v":3.1415926535897931},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B127,D127,E127,F127),\"\")","v":""},"","","","","",""]
[113,"x^(-3/4)*(1-x)^(-0.25)/(3-2*x)","FINITE_113","x",0,1,{"$f":"PI()*SQRT(2/3/SQRT(3))","v":1.949054259166747},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B128,D128,E128,F128),\"\")","v":""},"","","","","",""]
[114,"1/(5+4*COS(x))","FINITE_114","x",0,{"$f":"PI()","v":3.1415926535897931},1.0471975511964999,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B129,D129,E129,F129),\"\")","v":""},"","","","","",""]
[115,"LN(x)*SQRT(x/(1-x))","FINITE_115","x",0,1,-0.60678976350870495,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B130,D130,E130,F130),\"\")","v":""},"","","","","",""]
[116,"LN(ABS((TAN(x)+SQRT(7))/(TAN(x)-SQRT(7))))","FINITE_116","x",{"$f":"PI()/3","v":1.0471975511965976},{"$f":"PI()/2","v":1.5707963267948966},{"$f":"1.15192547054449/24*7*SQRT(7)","v":0.8889149278163524},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B131,D131,E131,F131),\"\")","v":""},"","","","","",""]
[117,"1/(1+25*x^2)","FINITE_117","x",0,1,{"$f":"0.2*ATAN(5)","v":0.2746801533890032},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B132,D132,E132,F132),\"\")","v":""},"","","","","",""]
[118,"COS(x)^3","FINITE_118","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"2/3","v":0.66666666666666663},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B133,D133,E133,F133),\"\")","v":""},"","","","","",""]
[119,"1/(1+SIN(x))","FINITE_119","x",0,{"$f":"PI()/4","v":0.78539816339744828},0.58578643726268997,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B134,D134,E134,F134),\"\")","v":""},"","","","","",""]
[120,"1/(1-x^4/2)","FINITE_120","x",0,1,1.1436672540694099,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B135,D135,E135,F135),\"\")","v":""},"","","","","",""]
[121,"1/(1+100*x^2)","FINITE_121","x",0,1,0.14711276743037299,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B136,D136,E136,F136),\"\")","v":""},"","","","","",""]
[122,"LN(x)/x","FINITE_122","x",1,2,0.240226506959101,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B137,D137,E137,F137),\"\")","v":""},"","","","","",""]
[123,"1/(EXP(x)-1)","FINITE_123","x",1,2,0.31326168751822298,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B138,D138,E138,F138),\"\")","v":""},"","","","","",""]
[124,"1/(1+x^2)","FINITE_124","x",-4,4,{"$f":"2*ATAN(4)","v":2.6516353273360651},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B139,D139,E139,F139),\"\")","v":""},"","","","","",""]
[125,"1/(1+SIN(x)^2)","FINITE_125","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()*SQRT(2)/4","v":1.1107207345395915},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B140,D140,E140,F140),\"\")","v":""},"","","","","",""]
[126,"SQRT(ABS(x^2-0.25))","FINITE_126","x",0,1,{"$f":"PI()/16+SQRT(3)/4-LN(2+SQRT(3))/8","v":0.4647425056259793},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B141,D141,E141,F141),\"\")","v":""},"","","","","",""]
[127,"LN(SIN(PI()*x))","FINITE_127","x",0,1,{"$f":"-LN(2)","v":-0.69314718055994529},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B142,D142,E142,F142),\"\")","v":""},"","","","","",""]
[128,"ABS(x-0.4)","FINITE_128","x",0,1,{"$f":"0.26","v":0.26},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B143,D143,E143,F143),\"\")","v":""},"","","","","",""]
[129,"EXP(-2*ABS(x-0.4))","FINITE_129","x",0,1,{"$f":"1-(EXP(-0.8)+EXP(-1.2))/2","v":0.62473841198528812},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B144,D144,E144,F144),\"\")","v":""},"","","","","",""]
[130,"LN(ABS(x-0.3))","FINITE_130","x",0,1,{"$f":"0.3*LN(0.3)+0.7*LN(0.7)-1","v":-1.6108643020548934},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B145,D145,E145,F145),\"\")","v":""},"","","","","",""]
[131,"1/(x+0.01)^5","FINITE_131","x",0,1,{"$f":"(10^8-1.01^-4)/4","v":24999999.759754915},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B146,D146,E146,F146),\"\")","v":""},"","","","","",""]
[132,"1/SQRT(x+0.0001)","FINITE_132","x",0,1,{"$f":"2*SQRT(1.0001)-1/50","v":1.9800999975001248},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B147,D147,E147,F147),\"\")","v":""},"","","","","",""]
[133,"1/(x+0.0001)","FINITE_133","x",0,1,{"$f":"LN(10001)","v":9.2104403669765169},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B148,D148,E148,F148),\"\")","v":""},"","","","","",""]
[134,"1/((230*x-30)^2+1)","FINITE_134","x",0,1,{"$f":"(ATAN(200)+ATAN(30))/230","v":1.3492485649467773E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B149,D149,E149,F149),\"\")","v":""},"","","","","",""]
[135,"1/(x+0.01)","FINITE_135","x",0,1,{"$f":"LN(101)","v":4.6151205168412597},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B150,D150,E150,F150),\"\")","v":""},"","","","","",""]
[136,"x*SIN(30*x)*COS(x)","FINITE_136","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"-60*PI()/899","v":-0.20967247966116526},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B151,D151,E151,F151),\"\")","v":""},"","","","","",""]
[137,"EXP(-x)*SIN(10*x)","FINITE_137","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"(1-EXP(-2*PI()))/10.1","v":9.8825005670127919E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B152,D152,E152,F152),\"\")","v":""},"","","","","",""]
[138,"x*(1-x)^2/(1+x)^3","FINITE_138","x",0,1,{"$f":"5*(0.7-LN(2))","v":3.4264097200273347E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B153,D153,E153,F153),\"\")","v":""},"","","","","",""]
[139,"x^12*(1-x)^12/16/(1+x^2)","FINITE_139","x",0,1,{"$f":"431302721/137287920-PI()","v":7.3842443271132652E-10},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B154,D154,E154,F154),\"\")","v":""},"","","","","",""]
[140,"x^12*(1-x)^12/16","FINITE_140","x",0,1,{"$f":"1/1081662400","v":9.2450287631334883E-10},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B155,D155,E155,F155),\"\")","v":""},"","","","","",""]
[141,"ATAN(SQRT(x^2+2))/SQRT(x^2+2)/(x^2+1)","FINITE_141","x",0,1,{"$f":"5*PI()^2/96","v":0.51404189589007077},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B156,D156,E156,F156),\"\")","v":""},"","","","","",""]
[142,"1/(1+x^2+x^4)","FINITE_142","x",0,1,{"$f":"LN(9)/8+PI()/SQRT(48)","v":0.72810291322558185},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B157,D157,E157,F157),\"\")","v":""},"","","","","",""]
[143,"(x+0.1)^5","FINITE_143","x",0,1,0.29526000000000002,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B158,D158,E158,F158),\"\")","v":""},"","","","","",""]
[144,"1/(x^2+0.0001)","FINITE_144","x",0,1,156.07966601082299,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B159,D159,E159,F159),\"\")","v":""},"","","","","",""]
[145,"SQRT(x*(1-x))","FINITE_145","x",0,1,0.39269908169872397,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B160,D160,E160,F160),\"\")","v":""},"","","","","",""]
[146,"1/(9+x^6)","FINITE_146","x",0,1,0.109445561283758,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B161,D161,E161,F161),\"\")","v":""},"","","","","",""]
[147,"(x+0.01)^5","FINITE_147","x",0,1,0.17692002509999999,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B162,D162,E162,F162),\"\")","v":""},"","","","","",""]
[148,"1/(1-0.99*x^4)","FINITE_148","x",0,1,2.06715614378431,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B163,D163,E163,F163),\"\")","v":""},"","","","","",""]
[149,"x*EXP(-3*x^2)","FINITE_149","x",0,1,0.15836882193868901,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B164,D164,E164,F164),\"\")","v":""},"","","","","",""]
[150,"x^2*LN(EXP(1)/x)","FINITE_150","x",0,1,{"$f":"4/9","v":0.44444444444444442},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B165,D165,E165,F165),\"\")","v":""},"","","","","",""]
[151,"(4*SQRT(2)-8*x^3-4*SQRT(2)*x^4-8*x^5)/(1-x^8)","FINITE_151","x",0,{"$f":"1/SQRT(2)","v":0.70710678118654746},{"$f":"PI()","v":3.1415926535897931},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B166,D166,E166,F166),\"\")","v":""},"","","","","",""]
[152,"1/(3-2*x)*1/SQRT(x*(1-x))","FINITE_152","x",0,1,{"$f":"PI()/SQRT(3)","v":1.8137993642342178},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B167,D167,E167,F167),\"\")","v":""},"","","","","",""]
[153,"COS(2*PI()*x)/SQRT(1-x)","FINITE_153","x",0,1,{"$f":"0.48825340607534","v":0.48825340607534001},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B168,D168,E168,F168),\"\")","v":""},"","","","","",""]
[154,"2*(1-x^2)/(TAN(0.5)^2+x^2)","FINITE_154","x",-1,1,{"$f":"4*(PI()-1-SIN(1))/SIN(1)","v":6.1802329123859581},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B169,D169,E169,F169),\"\")","v":""},"","","","","",""]
[155,"1/SQRT(1-0.5*SIN(x)^2)","FINITE_155","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"1.85407467730137","v":1.8540746773013701},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B170,D170,E170,F170),\"\")","v":""},"","","","","",""]
[156,"2*(1-x^2)/(COS(4*ATANH(x))+COSH(2))","FINITE_156","x",-1,1,{"$f":"0.711943822970598","v":0.71194382297059799},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B171,D171,E171,F171),\"\")","v":""},"","","","","",""]
[157,"ACOS(COS(PI()*x)^2)/3/SIN(PI()*x)+0.5","FINITE_157","x",0,1,{"$f":"0.995555497762367","v":0.99555549776236696},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B172,D172,E172,F172),\"\")","v":""},"","","","","",""]
[158,"SIN(x)","FINITE_158","x",0,{"$f":"PI()","v":3.1415926535897931},2,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B173,D173,E173,F173),\"\")","v":""},"","","","","",""]
[159,"SIN(x)*COS(x)","FINITE_159","x",0,1,{"$f":"SIN(1)^2/2","v":0.35403670913678559},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B174,D174,E174,F174),\"\")","v":""},"","","","","",""]
[160,"SQRT(2*x+7)","FINITE_160","x",1,9,{"$f":"98/3","v":32.666666666666664},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B175,D175,E175,F175),\"\")","v":""},"","","","","",""]
[161,"x^3*EXP(-x)","FINITE_161","x",0,5,{"$f":"4.40984450821582","v":4.4098445082158202},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B176,D176,E176,F176),\"\")","v":""},"","","","","",""]
[162,"SIN(10*x)*EXP(-x)","FINITE_162","x",0,10,{"$f":"0.099006252443586","v":9.9006252443586004E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B177,D177,E177,F177),\"\")","v":""},"","","","","",""]
[163,"1/(1+x^64)","FINITE_163","x",0,1,{"$f":"0.989366989363264","v":0.98936698936326395},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B178,D178,E178,F178),\"\")","v":""},"","","","","",""]
[164,"SQRT(x)/(x-1)-1/LN(x)","FINITE_164","x",0,1,{"$f":"0.0364899739785765","v":3.64899739785765E-2},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B179,D179,E179,F179),\"\")","v":""},"","","","","",""]
[165,"EXP(x^2*(1-x)^2)","FINITE_165","x",0,1,{"$f":"1.03414105175077","v":1.0341410517507701},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B180,D180,E180,F180),\"\")","v":""},"","","",{"$f":"IF($H$5=1,IF(AND(ISNUMBER(G180),ISNUMBER(H180)),IF(G180=0,ABS(ABS(G180)-ABS(H180)), ABS(ABS(G180)-ABS(H180))/ABS(G180)),\"\"),\"\")","v":""},{"$f":"IF($H$5=1,IF(AND(ISNUMBER(G180),ISNUMBER(H180)),IF(L180=0,15,IF(L180>1,0,IF(INT(ABS(LOG(L180)))>15,15,INT(ABS(LOG(L180)))))),\"\"),\"\")","v":""},{"$f":"IF($H$5=1,IF(OR(ISNUMBER(H180)=FALSE,M180=0),\"Cannot calculate\",\"\"),\"\")","v":""}]
[166,"LN(x)*SIN(10*x)","FINITE_166","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"-0.471793074421961","v":-0.471793074421961},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B181,D181,E181,F181),\"\")","v":""},"","","","","",""]
[167,"COS(8*SIN(x)-x)/PI()","FINITE_167","x",0,{"$f":"PI()","v":3.1415926535897931},{"$f":"0.234636346853914","v":0.23463634685391399},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B182,D182,E182,F182),\"\")","v":""},"","","","","",""]
[168,"x*SIN(10*x)*COS(x)","FINITE_168","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"-0.634665182543392","v":-0.63466518254339199},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B183,D183,E183,F183),\"\")","v":""},"","","","","",""]
[169,"23*COSH(x)/25-COS(x)","FINITE_169","x",-1,1,{"$f":"0.479428226688801","v":0.47942822668880097},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B184,D184,E184,F184),\"\")","v":""},"","","","","",""]
[170,"x^3*SIN(10*PI()*x)/SQRT(1-x^2)","FINITE_170","x",-1,1,{"$f":"-0.301833279121779","v":-0.30183327912177899},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B185,D185,E185,F185),\"\")","v":""},"","","","","",""]
[171,"COS(x)*LN(x)","FINITE_171","x",0,1,{"$f":"-0.946083070367183","v":-0.94608307036718298},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B186,D186,E186,F186),\"\")","v":""},"","","","","",""]
[172,"LN(1+x)*SIN(10*x)","FINITE_172","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"-0.197626807718717","v":-0.19762680771871699},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B187,D187,E187,F187),\"\")","v":""},"","","","","",""]
[173,"x^(PI()/4)*SIN(PI()/(8-4*x))","FINITE_173","x",0,2,{"$f":"1.01123909053","v":1.0112390905299999},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B188,D188,E188,F188),\"\")","v":""},"","","","","",""]
[174,"x^x","FINITE_174","x",0,1,{"$f":"0.783430510712134","v":0.78343051071213399},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B189,D189,E189,F189),\"\")","v":""},"","","","","",""]
[175,"x^-x","FINITE_175","x",0,1,1.29128599706266,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B190,D190,E190,F190),\"\")","v":""},"","","","","",""]
[176,"(4+COS(x))*LN(3+COS(x))","FINITE_176","x",0,{"$f":"PI()","v":3.1415926535897931},{"$f":"PI()*(3-SQRT(8)+4*LN((3+SQRT(8))/2))","v":13.980002011627681},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B191,D191,E191,F191),\"\")","v":""},"","","","","",""]
[177,"x^3-3*x^2","FINITE_177","x",-2,4,-12,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B192,D192,E192,F192),\"\")","v":""},"","","","","",""]
[178,"2*SQRT(1-x^2)","FINITE_178","x",-1,1,{"$f":"PI()","v":3.1415926535897931},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B193,D193,E193,F193),\"\")","v":""},"","","","","",""]
[179,"LN(x)^2 / (x^2+x+1)","FINITE_179","x",0,1,{"$f":"8*PI()^3 / (81*SQRT(3))","v":1.7680476235001594},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B194,D194,E194,F194),\"\")","v":""},"","","","","",""]
[180,"x^2 / SIN(x)^2","FINITE_180","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()*LN(2)","v":2.1775860903036022},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B195,D195,E195,F195),\"\")","v":""},"","","","","",""]
[181,"x^2/((1+x^4)*SQRT(1-x^4))","FINITE_181","x",0,1,{"$f":"PI()/8","v":0.39269908169872414},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B196,D196,E196,F196),\"\")","v":""},"","","","","",""]
[182,"SQRT(x)/SQRT(1-x)","FINITE_182","x",0,1,{"$f":"PI()/2/SIN(PI()/2)","v":1.5707963267948966},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B197,D197,E197,F197),\"\")","v":""},"","","","","",""]
[183,"LN(x)/(1+LN(x))^2","FINITE_183","x",1,{"$f":"EXP(1)","v":2.7182818284590451},{"$f":"EXP(1)/2-1","v":0.35914091422952255},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B198,D198,E198,F198),\"\")","v":""},"","","","","",""]
[184,"ATAN(x)/x/(x^2+1)","FINITE_184","x",0,1,{"$f":"PI()*LN(2)/8+0.915965594177219 /2","v":0.73018105837655978},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B199,D199,E199,F199),\"\")","v":""},"","","","","",""]
[185,"COS(3*x)^2/(5-4*COS(2*x))","FINITE_185","x",0,{"$f":"2*PI()","v":6.2831853071795862},{"$f":"3*PI()/8","v":1.1780972450961724},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B200,D200,E200,F200),\"\")","v":""},"","","","","",""]
[186,"x*TAN(x)","FINITE_186","x",0,{"$f":"PI()/4","v":0.78539816339744828},0.18578453580065901,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B201,D201,E201,F201),\"\")","v":""},"","","","","",""]
[187,"x^2/(1-COS(x))","FINITE_187","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()*LN(2)-PI()^2/4+4*0.915965594177219","v":3.3740473667401387},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B202,D202,E202,F202),\"\")","v":""},"","","","","",""]
[188,"x^4*(1-x)^4/(1+x^2)","FINITE_188","x",0,1,{"$f":"22/7-PI()","v":1.2644892673496777E-3},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B203,D203,E203,F203),\"\")","v":""},"","","","","",""]
[189,"(x^2-x)^2/(x^3-3*x+1)^2","FINITE_189","x",-100,-10,{"$f":"11131110/107634259","v":0.1034160508319196},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B204,D204,E204,F204),\"\")","v":""},"","","","","",""]
[190,"PI()/2*COSH(x)*SIN(EXP(PI()/2*SINH(x)))","FINITE_190","x",-2,2,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B205,D205,E205,F205),\"\")","v":""},"","","","","",""]
[191,"1/PI()/SQRT(1-x^2)","FINITE_191","x",-1,1,{"$f":"1/PI()*(ASIN(1)+PI()/2)","v":1},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B206,D206,E206,F206),\"\")","v":""},"","","","","",""]
[192,"1/4/LN(2)*LN((1+x)/(1-x))","FINITE_192","x",-1,0.5,{"$f":"1/4/LN(2)*(1.5*LN(1.5)+0.5*LN(0.5))-0.5","v":-0.40563906222956642},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B207,D207,E207,F207),\"\")","v":""},"","","","","",""]
[193,"(1+x)^2*EXP(-x)/(1+x^2)^2","FINITE_193","x",0,1,{"$f":"1-EXP(-1)/2","v":0.81606027941427883},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B208,D208,E208,F208),\"\")","v":""},"","","","","",""]
[194,"LN(1-x)/x","FINITE_194","x",0,1,{"$f":"-(PI()^2/6)","v":-1.6449340668482264},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B209,D209,E209,F209),\"\")","v":""},"","","","","",""]
[195,"x/(1-x)","FINITE_195","x",0,0.5,{"$f":"LN(2)-1/2","v":0.19314718055994529},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B210,D210,E210,F210),\"\")","v":""},"","","","","",""]
[196,"1/(1+TAN(x)^SQRT(2))","FINITE_196","x",0,{"$f":"PI()/2","v":1.5707963267948966},{"$f":"PI()/4","v":0.78539816339744828},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B211,D211,E211,F211),\"\")","v":""},"","","","","",""]
[197,"SQRT(1-x^4)","FINITE_197","x",-1,1,{"$f":"SQRT(PI())*0.906402477055477 / 0.919062526848883","v":1.7480383695280801},{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B212,D212,E212,F212),\"\")","v":""},"","","","","",""]
[198,"1/((x-0.3)^2+0.01)+1/((x-0.9)^2+0.04)-6","FINITE_198","x",0,1,29.858325395498699,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B213,D213,E213,F213),\"\")","v":""},"","","","","",""]
[199,"COS(x^2)/SQRT(1-x^2)","FINITE_199","x",-1,1,2.5873677615517798,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B214,D214,E214,F214),\"\")","v":""},"","","","","",""]
[200,"EXP(2*x)","FINITE_200","x",0,0.5,0.85914091422952299,{"$f":"IF($H$5=1,QUAD_ROMBERG_GD(B215,D215,E215,F215),\"\")","v":""},"","","","","",""]

{"sheet":"CHART USAGE","index":1,"n_rows":18,"n_cols":2,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[null,"FUNCTION PLOTTER ON THE ROMBERG GD WORKSHEET:"]
[]
[null,"The function plotting chart on the ROMBERG GD worksheet is included for convenience to provide an easy way to view the plot of a selected function over the specified interval of integration."]
[null,"For convenience and ease of use, it makes use of and shares the function input data in Columns A, B, D, E and F used by the Romberg program, although it is completely independent from the Romberg program."]
[null,"The function plotter plots the functions entered in Column B."]
[null,"To enable (show) the plotting chart, after enabling macros, click the Click To Show Chart button, then select the function to be plotted from the list using the two arrow buttons."]
[null,"NOTE: A small pause may occur on the first up-down button click, but only for the first time."]
[]
[null,"The function plotting chart is enabled or disabled by a button. By default, the chart is disabled (hidden)."]
[null,"While the function plot is showing, the data used by the chart is shown as a highlighted bar of colour in the function listing, and the highlighted data in the functions list is duplicated in cells A11:F11 to confirm the data being plotted."]
[null,"Click the up and down arrow buttons to change the selected function."]
[null,"The plot is automatically generated after the function selection is made, or after any change to the data used by the selected function is made, such as one of the limits."]
[null,"The function to be plotted may also be selected by directly entering the respective function number, shown in column A, into cell A11."]
[null,"Do Not enter data into cells B11:F11. These are not input cells."]
[null,"To disable (hide) the chart, click the Click to Hide Chart button."]