Mulitvariable Calculus Four Dimensional Sphere

[Girth]

Homework Statement

Use double polar coordinates x=rcosθ y=rsinθ z=scosφ w=ssinφ in R^4
to compute the 4-dimensional volume of the ball x^2 +y^2 +z^2+w^2 = R^22. The attempt at a solution
I first substituted the polar coordinates into the given equation getting: r^2cos^2(θ)+r^2sin^2(θ)+s^2cos^2(φ)+r^2sin^2(φ) = R^2
this simplified to r^2 + s^2 = R^2 using the identity: cos^2(θ)+sin^2(θ)=1
After this I'm confused with where to go. Any tips would help, thanks.

 

[jedishrfu]

Homework Statement

Use double polar coordinates x=rcosθ y=rsinθ z=scosφ w=ssinφ in R^4
to compute the 4-dimensional volume of the ball x^2 +y^2 +z^2+w^2 = R^2


2. The attempt at a solution
I first substituted the polar coordinates into the given equation getting: r^2cos^2(θ)+r^2sin^2(θ)+s^2cos^2(φ)+r^2sin^2(φ) = R^2
this simplified to r^2 + s^2 = R^2 using the identity: cos^2(θ)+sin^2(θ)=1
After this I'm confused with where to go. Any tips would help, thanks.

To find the volume I think you must setup a 4D integral similar to how one finds the volume of a 3D sphere:

http://en.wikipedia.org/wiki/N-sphere