Integral "int" function not evaluating
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Why is the "int" function not evaluating my integral? The "r" variable still has the "int" in it.
clear
clc
theta_s = 0:0.5:pi/2;
syms theta_v phi
for i = 1:length(theta_s)
integ2(i) = ((((1/(2*pi))*((pi-phi)*cos(phi) + sin(phi))*tan(theta_s(i))*tan(theta_v)-(1/pi)*(tan(theta_s(i))+tan(theta_v)+sqrt(tan(theta_v)^2 + tan(theta_s(i))^2 - 2*tan(theta_s(i))*tan(theta_v)*cos(phi)))))*cos(theta_v)*sin(theta_v));
r(i)= int((integ2(i)), theta_v, [0 pi/2]);
end
1 个评论
Walter Roberson
2022-3-3
What reason do you have to lead you to expect that there is a closed form integral?
采纳的回答
David Hill
2022-3-3
theta_s = 0:0.5:pi/2;
syms theta_v
phi=pi/6;%choose a phi or loop for various values of phi
for i = 1:length(theta_s)
integ2(i) = ((((1/(2*pi))*((pi-phi)*cos(phi) + sin(phi))*tan(theta_s(i))*tan(theta_v)-(1/pi)*(tan(theta_s(i))+tan(theta_v)+sqrt(tan(theta_v)^2 + tan(theta_s(i))^2 - 2*tan(theta_s(i))*tan(theta_v)*cos(phi)))))*cos(theta_v)*sin(theta_v));
r(i)= vpaintegral((integ2(i)), theta_v, [0 pi/2]);
end
6 个评论
Ali Almakhmari
2022-3-3
Torsten
2022-3-3
If "int" does not return an analytical expression for the integral in terms of phi, you'll have to be satisfied with an evaluation for different numerical values of phi.
AndresVar
2022-3-4
@Ali Almakhmari the square root part is too complicated to find a simplified closed form. Could there be a typo or maybe use some identity to simplify?
Ali Almakhmari
2022-3-4
David Hill
2022-3-4
Works fine.
theta_s = 0:0.5:pi/2;
syms theta_v phi
for i = 1:length(theta_s)
integ2(i) = ((((1/(2*pi))*((pi-phi)*cos(phi) + sin(phi))*tan(theta_s(i))*tan(theta_v)-(1/pi)*(tan(theta_s(i))+tan(theta_v)+sqrt(tan(theta_v)^2 + tan(theta_s(i))^2 - 2*tan(theta_s(i))*tan(theta_v)*cos(phi)))))*cos(theta_v)*sin(theta_v));
r(i)= vpaintegral(vpaintegral((integ2(i)), theta_v, [0 pi/2]),phi,[0 pi]);
end
Walter Roberson
2022-3-6
By the way, integrating first with respect to phi is faster.
At one point I saw a closed form solution for integration with respect to phi, but I was not able to reproduce that later.
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