Need help with this calc 3 question

Question

Answer 1

I come up with the integral from z= 1/2 to 1, integral of y=0 to sqrt(1-z²), integral from x = 0 to sqrt(1-z²-y²) of (x²+y³ - z) dxdydz.

1st integration in x gives (1-z²-y²)^3/2/3 + y³(1-z²-y²)^1/2 - z(1-z²-y²)^1/2

Due to time constraints, I have to stop here.

If it was x²+y² switching to cylindrical coordinates would make this easy. Even as is, switching to cylindrical makes sense.