how to do double integration including symbolic ??

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

Answer 1

[Walter Roberson]

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)

[gourav pandey]

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)

[Walter Roberson]

Maple says the result is 0.

Answer 2

[Matt J]

If you are integrating a symbolic expression, you should use int()

https://www.mathworks.com/help/symbolic/sym.int.html

You should remove "@(theta,omega1)" from the definition of temp. It makes no sense to have it there if theta and omega1 are symbolic.

[gourav pandey]

theta and omega1 are function handle. Thank you Matt, i will do the changes. Thank you