Unable to convert expression into double array

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.

[KSSV]

Read about vpasolve

Answer 1

[Ameer Hamza]

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)

[Sikai Wu]

vpaintegral(E1,x,[100 300])

Thanks a lot for your advice, I use this code to get the results.

[Ameer Hamza]

I am glad to be of help!

Answer 2

[Walter Roberson]

[I was just about to post this when I had a network outage. I just got back to my computer... so it is a bit late.]

MATLAB simply is not powerful enough to integrate that. It does have a closed-form integral, involving a number of erf() of complex values.

You can use vpaintegral() .

It is obvious from the expression that you integrated an expression that had a number of floating point constants. Floating point constants express uncertainty -- for example 1.23 expresses "some indeterminate number between 1225/1000 inclusive and 1235/1000 exclusive". When you have floating point constants in a int() then you are almost certainly doing the wrong thing -- asking for an exact solution to a problem whose values are not exactly known.

[Walter Roberson]

Sikau Wu comments

The answer analysis the problem clearly and tell me how to overcome it.

[Walter Roberson]

E1 and E2 both do have closed form solutions involving a lot of large rational numbers and a number of erf() calls such as erf(3/8*2^(1/2)*(1i*pi+4)) -- but MATLAB just is not powerful enough to calculate it without further guideance.

Answer 3

[Sikai Wu]

Thanks a lot for your help. I got the points why it happened. Maybe it is luckly for me to calculte the result by int() for E2 function.