# Volume under a parabaloid

Use polar coordinates to find the volume under $f(x,y)=1+(x^2+y^2)$ and over the disk $x^2+y^2\leq2$.

f(r,theta)=1+r^2 and r^2<=2
int_0^(2pi)int_0^sqrt(2)(1+r^2)rdrd theta
int_0^(2pi)int_0^sqrt(2)r+r^3drd theta
int_0^(2pi)r^2/2+r^4/4 |_0^sqrt(2)
int_0^(2pi)2d theta
2 theta|_0^(2pi)=4pi