how to do double integration including symbolic ??

Question

gourav pandey 2021-8-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/899097-how-to-do-double-integration-including-symbolic

评论： Walter Roberson 2021-8-16

clc; 
clear;
close all;
syms  theta omega1 P_t Q_t P_n Q_n Pc2 Pc3 Pc4 Ps2 Ps3 Ps4 Qc2 Qc3 Qc4 Qs2 Qs3 Qs4 
a1=1;
h1=5;
temp=@(theta,omega1) -omega1.^2.*exp(-abs(omega1).*(cos(theta) + 5)).*((Qs2.*((28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (141110627044806525.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./4503599627370496 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./18014398509481984) + Pc2.*((9407375136320435.*omega1.^(5./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2)./omega1.^2 - (cos(theta) + 5).*((Qs2.*((28222125408961305.*omega1.^(3./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) - (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./2))./4503599627370496 + (28222125408961305.*omega1.^(1./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./2 - (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./2251799813685248 + (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2 + (5.*pi.*Q_n.*omega1.*exp(-omega1))./2)./omega1 - (abs(omega1).*(Qs2.*((28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (141110627044806525.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./4503599627370496 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./18014398509481984) + Pc2.*((9407375136320435.*omega1.^(5./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2))./omega1.^2))
Fun = integral2(@(theta,omega1) (temp(theta,omega1).*cos(omega1.*a1.*sin(theta))),0,2*pi,0,inf)

%%%%%%%%%%% Please help...I'm a beginner in matlab. i tried to use "double" but getting error. Please help

%%%%%%%%% Thank you in advance

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Answer 1

Walter Roberson 2021-8-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/899097-how-to-do-double-integration-including-symbolic#answer_767967

在 MATLAB Online 中打开

There is no possible way to use integral() or integral2() when the expression to be integrated includes unresolved symbolic variables. integral() and integral2() are strictly numeric integration.

The below may take a fair while. You can get through result_inner in a quite reasonable time, but the last step is not fast.

syms  theta omega1 P_t Q_t P_n Q_n Pc2 Pc3 Pc4 Ps2 Ps3 Ps4 Qc2 Qc3 Qc4 Qs2 Qs3 Qs4 
assume(theta >= 0 & omega1 >= 0)
a1=1;
h1=5;
temp_sym = simplify(str2sym('-omega1.^2.*exp(-abs(omega1).*(cos(theta) + 5)).*((Qs2.*((28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (141110627044806525.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./4503599627370496 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./18014398509481984) + Pc2.*((9407375136320435.*omega1.^(5./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2)./omega1.^2 - (cos(theta) + 5).*((Qs2.*((28222125408961305.*omega1.^(3./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) - (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./2))./4503599627370496 + (28222125408961305.*omega1.^(1./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./2 - (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./2251799813685248 + (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2 + (5.*pi.*Q_n.*omega1.*exp(-omega1))./2)./omega1 - (abs(omega1).*(Qs2.*((28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (141110627044806525.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./18014398509481984 - (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./4503599627370496 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./18014398509481984) + Pc2.*((9407375136320435.*omega1.^(5./2).*((5.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./(2.*omega1.^(1./2)) + (2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./2))./18014398509481984 - (28222125408961305.*omega1.^(3./2).*((2.^(1./2).*omega1.^(1./2).*pi.^(1./2).*exp(-omega1))./2 + (3.*2.^(1./2).*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./(2.*omega1.^(1./2))))./18014398509481984 - (28222125408961305.*2.^(1./2).*pi.^(1./2).*exp(-omega1))./4503599627370496 + (28222125408961305.*2.^(1./2).*omega1.^2.*pi.^(1./2).*exp(-omega1).*(3./omega1 + 3./omega1.^2 + 1))./36028797018963968 + (84666376226883915.*2.^(1./2).*omega1.*pi.^(1./2).*exp(-omega1).*(1./omega1 + 1))./18014398509481984 - (9407375136320435.*2.^(1./2).*omega1.^3.*pi.^(1./2).*exp(-omega1).*(6./omega1 + 15./omega1.^2 + 15./omega1.^3 + 1))./36028797018963968) + Q_n.*pi.*exp(-omega1).*((5.*omega1)./2 + 5./2) - (5.*pi.*P_t.*omega1.*exp(-omega1))./2))./omega1.^2))'))
inner = (temp_sym.*cos(omega1.*a1.*sin(theta)))
inner_sym = simplify(inner)
result_inner = int(inner_sym, theta, 0, 2*pi)
result = int(result_inner, omega1, 0,inf)

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gourav pandey 2021-8-16

i will note it down the point mention by you. Thank you Walter but not getting the answer from the code provided by you.

result =

int(int(-(5*cos(omega1*sin(theta))*exp(-omega1*(cos(theta) + 6))*(pi*(9007199254740992*Q_n - 9007199254740992*P_t*omega1 + 54043195528445952*Q_n*omega1 + 9007199254740992*Q_n*omega1*cos(theta)) - 2^(1/2)*pi^(1/2)*(5644425081792261*Pc2 - 11288850163584522*Qs2 + 11288850163584522*Pc2*omega1 - 45155400654338088*Qs2*omega1 - 84666376226883915*Pc2*omega1^2 + 95955226390468437*Qs2*omega1^2 - 139229152017542438*Qs2*omega1^3 + 18814750272640870*Qs2*omega1^4 - 16933275245376783*Pc2*omega1^2*cos(theta) + 22577700327169044*Qs2*omega1^2*cos(theta) - 28222125408961305*Qs2*omega1^3*cos(theta) + 3762950054528174*Qs2*omega1^4*cos(theta) + 5644425081792261*Pc2*omega1*cos(theta) - 11288850163584522*Qs2*omega1*cos(theta))))/18014398509481984, theta, 0, 2*pi), omega1, 0, Inf)