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 !