Volume using double integral (polar coordiantes)

[whynot314]

Homework Statement

use a double integral to find the volume of the solid bounded by.

z=x^2+2y^2 and z=12-2x^2-y^2

I want to change variables using polar coordinates, I know its the top minus the bottom, and the intersection between the two is a circle radius 2.

The Attempt at a Solution

I want to make sure i have the correct set up

\int^{2\pi}_{0} \int^{2}_{0} (12-3r^{2})rdrd\theta

 

[SammyS]

Homework Statement

use a double integral to find the volume of the solid bounded by.

z=x^2+2y^2 and z=12-2x^2-y^2

I want to change variables using polar coordinates, I know its the top minus the bottom, and the intersection between the two is a circle radius 2.

The Attempt at a Solution

I want to make sure i have the correct set up

\int^{2\pi}_{0} \int^{2}_{0} (12-3r^{2})rdrd\theta

That looks good !