# Math Help - Volume Integral

1. ## Volume Integral

Find the volume of the region in $\mathbb{R}^3$ that is bounded by the paraboloid $z=x^2+y^2$, the cylinder $x^2+y^2=1$ and the plane $z=0$.

Do I need to work out $\int_0^1 \int_0^{\sqrt{1-x^2}} \int_0^{x^2+y^2}~dz~dy~dx$?

2. Notice the region of integration is the unit circle so you would have to multiply

by 4

However it is easier i you use cylindrical coordinates

See attachment