Computing integral over a sphere

[PsychonautQQ]

Homework Statement

Computer the integral of f(x,y,z) = x^2+y^2 over the sphere S of radius 4 centered at the origin.

The Attempt at a Solution

so if the parameters for a sphere are in terms of (p,θ,∅)
,
triple integral (p^2((psin∅cosθ)^2+(psin∅sinθ)^2))dpdθd∅)

where the boundaries on dp is 0 to 4, and then dθ and d∅ are both 0 to 2∏

am I on the correct track here?

 

[LCKurtz]

Homework Statement

Computer the integral of f(x,y,z) = x^2+y^2 over the sphere S of radius 4 centered at the origin.

The Attempt at a Solution

so if the parameters for a sphere are in terms of (p,θ,∅)
,
triple integral (p^2((psin∅cosθ)^2+(psin∅sinθ)^2))dpdθd∅)

where the boundaries on dp is 0 to 4, and then dθ and d∅ are both 0 to 2∏

am I on the correct track here?

Your question doesn't make clear whether you are asked to do a surface integral over the surface of the sphere or a volume integral over the solid sphere. In either case, you wouldn't integrate both $\phi$ and $\theta$ from $0$ to $2\pi$. Also, your volume element is incorrect.