MATLAB: Unable to convert expression into double array

integration

syms x
% E1 = -(574936417714633*exp(-(x - 150)^2/5000)*((8183344744316655*cos((pi*x)/100))/288230376151711744 - (7103677074291021*cos((pi*x)/140))/18014398509481984 + (2282254577390745*cos((pi*x)/175))/281474976710656 + (209433984667347*cos((pi*x)/350))/17592186044416 - (4635952013778339*cos((3*pi*x)/350))/18014398509481984 + (3116202096570579*cos((pi*x)/700))/70368744177664 - (1592500999883349*cos((3*pi*x)/700))/70368744177664 + (5286183364156013*sin((pi*x)/100))/2305843009213693952 - (5282470715436721*sin((pi*x)/140))/2251799813685248 + (4930148030865465*sin((pi*x)/175))/1125899906842624 - (3313419311544189*sin((pi*x)/350))/70368744177664 + (5052137790519353*sin((3*pi*x)/350))/18014398509481984 + (8004373085987215*sin((pi*x)/700))/140737488355328 + (5597432279575929*sin((3*pi*x)/700))/562949953421312 - 2888206238924633/70368744177664))/72057594037927936
E2 = -(574936417714633*exp(-(x - 150)^2/5000)*((8823814544749061*cos((pi*x)/100))/2417851639229258349412352 - (66451917855713*cos((pi*x)/50))/37778931862957161709568 - (7396681414274859*cos((pi*x)/40))/4835703278458516698824704 - (6468445020191767*cos((3*pi*x)/100))/9671406556917033397649408 + (1163326145497647*cos((pi*x)/200))/151115727451828646838272 - (804955420280903*cos((3*pi*x)/200))/19342813113834066795298816 - (8501245438962469*cos((7*pi*x)/200))/77371252455336267181195264 + (4739840162395179*sin((pi*x)/40))/1208925819614629174706176 + (5198608414617587*sin((pi*x)/50))/604462909807314587353088 + (4351639281487411*sin((pi*x)/100))/302231454903657293676544 + (2791257967313459*sin((3*pi*x)/100))/2417851639229258349412352 + (1458476753937829*sin((pi*x)/200))/151115727451828646838272 + (4006877253789739*sin((3*pi*x)/200))/302231454903657293676544 + (7621631973170679*sin((7*pi*x)/200))/38685626227668133590597632 + 2646175801254393/604462909807314587353088))/72057594037927936
 
Rone=int(E2,x,100, 300)
double(Rone)
I want to get the integrate value of E1, but when I run the codes, it said that Unable to convert expression into double array. But when I calculated the integrate value of E2, I can get the result. Could you please tell me how to get the integratation value of E1? Thanks a lot for your advice.

Best Answer

It seems that some terms in your integral cannot be solved symbolically therefore MATLAB throws this error. You can try to calculate the numerical integral using vpaintegral()
syms x
E1 = -(574936417714633*exp(-(x - 150)^2/5000)*((8183344744316655*cos((pi*x)/100))/288230376151711744 - (7103677074291021*cos((pi*x)/140))/18014398509481984 + (2282254577390745*cos((pi*x)/175))/281474976710656 + (209433984667347*cos((pi*x)/350))/17592186044416 - (4635952013778339*cos((3*pi*x)/350))/18014398509481984 + (3116202096570579*cos((pi*x)/700))/70368744177664 - (1592500999883349*cos((3*pi*x)/700))/70368744177664 + (5286183364156013*sin((pi*x)/100))/2305843009213693952 - (5282470715436721*sin((pi*x)/140))/2251799813685248 + (4930148030865465*sin((pi*x)/175))/1125899906842624 - (3313419311544189*sin((pi*x)/350))/70368744177664 + (5052137790519353*sin((3*pi*x)/350))/18014398509481984 + (8004373085987215*sin((pi*x)/700))/140737488355328 + (5597432279575929*sin((3*pi*x)/700))/562949953421312 - 2888206238924633/70368744177664))/72057594037927936
% E2 = -(574936417714633*exp(-(x - 150)^2/5000)*((8823814544749061*cos((pi*x)/100))/2417851639229258349412352 - (66451917855713*cos((pi*x)/50))/37778931862957161709568 - (7396681414274859*cos((pi*x)/40))/4835703278458516698824704 - (6468445020191767*cos((3*pi*x)/100))/9671406556917033397649408 + (1163326145497647*cos((pi*x)/200))/151115727451828646838272 - (804955420280903*cos((3*pi*x)/200))/19342813113834066795298816 - (8501245438962469*cos((7*pi*x)/200))/77371252455336267181195264 + (4739840162395179*sin((pi*x)/40))/1208925819614629174706176 + (5198608414617587*sin((pi*x)/50))/604462909807314587353088 + (4351639281487411*sin((pi*x)/100))/302231454903657293676544 + (2791257967313459*sin((3*pi*x)/100))/2417851639229258349412352 + (1458476753937829*sin((pi*x)/200))/151115727451828646838272 + (4006877253789739*sin((3*pi*x)/200))/302231454903657293676544 + (7621631973170679*sin((7*pi*x)/200))/38685626227668133590597632 + 2646175801254393/604462909807314587353088))/72057594037927936
 
Rone=vpaintegral(E1,x,100, 300)
double(Rone)
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