Integrating Norm in Unit Ball in Rn-2

[Matthollyw00d]

\int|x|² with respect to the vector x in the unit ball in R^n-2

I'm dealing with volumes of unit balls in Rⁿ and after applying a change of variable to the last 2 components and Fubini's Theorem, I get that integral and can't find a way to integrate it. Any help on this?

 

[rochfor1]

Generalized spherical coordinates.

 

[Matthollyw00d]

Would that just make |x|²=r²? I've never worked with generalized spherical coordinates before, so could you elaborate a bit?

 

[Matthollyw00d]

Nevermind, I found an alternate way.