Use the double integral in polar coordinates to find the volume of the solid bounded by the graphs of the given equuations :
z= x^2+y^2+3 , z=0 , x^2+y^2=1
The integrand $\displaystyle x^2+y^2+3$
is the height above the xy plane. As we integrate over the area in the xy plane we get the volume between the surface and the plane z=0.
The 2d equivelent is finding the area under the curve $\displaystyle y=x^2$ from x=2 to x=4. We use the fact that it is bounded below by y=0 to get the area between the curve and the x axis.
I hope this Helps.
Brett