# Math Help - Paraboliod Help

1. ## Paraboliod Help

I'm supposed to find the volume of the solid enclosed by $z=x^2+3y^2$ and the planes x=0, y=1, y=x and z=0. I'm not even sure what that looks like though, hence I don't know what the limits of integration are, or even what to integrate. Can someone help me get started?

2. In order to be able to solve these kinds of volume questions, you must learn to draw or at least visualize the area you are finding. I will help you here, but eventually you're going to have to be able to do it yourself.

First of all the z=0 bound is unnecessary as this elliptic paraboloids vertex is at (0,0,0). z is bounded above by your function. y goes from x to 1, and x goes from 0 to infinity.

$\displaystyle\int_0^\infty\displaystyle\int_x^1 x^2+3y^2\,dy\,dx$

EDIT: These bounds could also describe an area where y goes from x to 1 and x goes from -1 to 0, which may be what your professor is looking for since its supposed to be an enclosed volume