Integrated Integrals

[engineertobe]

Find the volume of the solid lying under the elliptic paraboloidx^2/4+y^2/16+z=1
(counting volume above z=0 as positive and that below z=0 as negative), bounded by the planes x=−2, x=2, y=−1 andy=1.

I assume I used integrated integrals, but how do I go about setting them up?

 

[galactus]

Solve the paraboloid equation for z:

\(\displaystyle z=1-\frac{x^{2}}{4}-\frac{y^{2}}{16}\)

The limits of integration are given.

\(\displaystyle \displaystyle \int_{-2}^{2}\int_{-1}^{1}(1-\frac{x^{2}}{4}-\frac{y^{2}}{16})dydx\)