# Calculating double integral of two variable

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Ismael Gilles Durand on 19 Jun 2020
Edited: Devineni Aslesha on 22 Jun 2020
I am having some issues calculation a double integral with two variable. my function F= {{sinc^2(X)sinc^2(Y)} *{sin^2(phi)+cos^2(theta)cos^2(phi)}}(sin(theta)).
I define X=(pi/2).*sin(theta).*cos(phi) and Y=(pi/2).*sin(theta).*sin(phi); and theta=[0 pi/2]; phi=[0 2*pi].
So, I have started
syms X Y theta phi
theta=linspace(0,pi/2);
phi=linspace(0,2*pi);
X=(pi/2).*sin(theta).*cos(phi);
Y=(pi/2).*sin(theta).*sin(phi);
func1=(sinc(X/pi).*sinc(Y/pi)).^2;
func2={(sin(theta))^2}+{cos(theta)cos(phi)}^2;
func=func1*func2;
func3=sin(theta);
Function1=vpa(int(func,0,2*pi),5)*vpa(int(func3,0,pi/2),5)
But I have also tried to rewrite
syms X Y theta phi
X=(pi/2).*sin(theta).*cos(phi);
Y=(pi/2).*sin(theta).*sin(phi);
Function1=@(theta,phi) ((sinc(X/pi).*sinc(Y/pi))^2 *((sin(phi))^2+(cos(theta)*cos(phi))^2))*(sin(theta));
E=integral2(Function1,0,pi/2,0,2*pi)

Devineni Aslesha on 22 Jun 2020
Edited: Devineni Aslesha on 22 Jun 2020
Hi Ismael,
To calculate the double integral of a two variable function, integral2 accepts only numeric variables. So, the entire function with two variable is defined as a single inline executable expression (anonymous function handles) as shown below.
Function1 = @(theta,phi) (((sinc((pi/2).*sin(theta).*cos(phi)).*sinc((pi/2).*sin(theta).*sin(phi))).^2).*((sin(phi)).^2+(cos(theta).*cos(phi)).^2)).*(sin(theta));
E = integral2(Function1,0,pi/2,0,2*pi)
##### 2 CommentsShowHide 1 older comment
Devineni Aslesha on 22 Jun 2020
int can accept both numeric and symbolic variables, whereas integral2 accepts only numeric variables as integral2 solves the integral numerically. Also, thanks for pointing that out, I can edit the answer specific to integral2.

R2019a

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