Calculate double integrate of sin

I want to calculate this:

But I can't write it correctly. I get the gamma function all the time.

It seems to be something like this:

syms theta rho n

f = sin(rho)^(n + 2)*sin(theta)^(n + 1)

I1 = int(f,rho,0,pi)

I2 = int(I1,theta,0,pi)

But the answer is:

(2*2^(2*n)*gamma(n/2)^2*gamma(n/2 + 1/2)^2*(n/2 + 1/2)^2)/(gamma(n)^2*(n + 1)^2*(n + 2))

When, i hope the return was:

2pi/n+2

Thanks in advance.

[Sam Chak]

@Ana Laura, Erm... I believe the Gamma Γ symbols (not gamma γ) are the Gamma function. I don't use it often, but I encountered it in the Riemann zeta function.

Answer 1

[Dyuman Joshi]

You can simplify the expression obtained -

syms theta rho n
f = sin(rho)^(n + 2)*sin(theta)^(n + 1);
I1 = int(f,rho,0,pi);
I2 = int(I1,theta,0,pi)

I2 = 

%Output
out = simplify(I2)

out = 

[Ana Laura]

Thanks very much. It's perfect!!

[Torsten]

You can also write the double integral as the product of two one-dimensional integrals:

syms rho n
f = int(sin(rho)^(n + 2),rho,0,pi)*int(sin(rho)^(n + 1),rho,0,pi)

f = 

simplify(f)

ans =