# Volume under the elliptic paraboloid

1. Nov 6, 2008

Greetings again,

this is another I'm stuck on...

Calculate the volume under the elliptic paraboloid z = x^{2} + 4y^{2} and over the rectangle R = [-1, 1] \times [-4, 4].

I'm not sure how to find the limits of z for the triple integral. Can I somehow integrate the function z, and only do a double integral? Perhaps going from -1, 0 and -4, 0 and then double it?

2. Nov 6, 2008