I need to find the volume of the region :
$$R=\{(x,y,z)| \space 0 \le (x-1)^2+y^2 \le z(1-z)\}$$
I don't understand the region. Is it the volume outside the cylinder and inside a sphere? Can you give me some hints in order to set up the integral?
Answer : $\frac{\pi}{6}$
The left inequality is always true for sum of squares is greater than zero.
The right inequality represents a sphere of radius $\frac{1}{2}$. Hence the volume of the region is $\frac{4}{3}\pi(\frac{1}{2})^3 = \frac{\pi}{6}$.