Calculating double integral of two variable

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)

Answer 1

[Devineni Aslesha]

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)

For more information, refer the following link

https://www.mathworks.com/help/matlab/ref/function_handle.html

[madhan ravi]

The first statement contradicts the fact that int(...) with two calls exist if there’s an explicit solution.

[Devineni Aslesha]

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.