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"Find the mass of part of the solid sphere x^2 + y^2 + z^ 2 ≤ 25 in the 1st octant x ≥ 0, y ≥ 0, z ≥ 0 where mass density is f (x, y, z ) = (x^2 + y^2 + z^2 )^3/2 ."

3.

These problems are really stumping me! I need somebody to work it out/explain it to me! What will the limits of integration be for the following question? What do i integrate? I know I need to transform it to spherical coordinates... but beyond that I'm lost.

I know it's a triple integral:

m = ∫∫∫(x^2 + y^2 + z^2)^3/2 dzdydx

transforming to spherical co-ordinates:

0 ≤ rho ≤ 5

0 ≤ theta ≤ ??? (how do I figure this out?)

0 ≤ phi ≤ ????? (ditto)

dzdydx = rho^2 sinphi drho dphi dtheta

What does f (x, y,z) transform to and how do I figure it out?

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# Homework Help: Triple integration w/spherical coordinates

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