Compute the triple integral of f(x, y, z) = z over the region F below the sphere x2 + y2 + z2 = 8 and above the triangular region in the xy-plane bounded by x = 0, y = 2, and y = x.

I suppose "below the sphere" means "inside" it, or below the upper half of it. The integral is

where

Evaluating the integral in Cartesian coordinates is straightforward enough to not require changing coordinates:

x=30

step-by-step explanation: