volume using polar

[teh_antiderivative]

Hello! I was just going through my calculus homework, when I came across a problem I thought I had passed long ago--VOLUME. It was buried under a sea of polar review problems. The question is as follows:

find the volume of the solid generated by revolving the region enclosed by the ellipse 9x^2 + 4y^2 = 36, by revolving it about the x-axis, and the y-axis.

Now, I have not done any work on this yet--I'm not quite sure where to start. Should I convert the cartesian equation into polar or parametric? Any help would be appreciated.

 

[skeeter]

it's not that difficult using cartesian coordinates ... in fact, it's pretty simple.

around the x-axis

\(\displaystyle \L V = 2\pi \int_0^2 9\left(1 - \frac{x^2}{4}\right)dx\)

around the y-axis

\(\displaystyle \L V = 2\pi \int_0^3 4\left(1 - \frac{y^2}{9}\right)dy\)

 

[teh_antiderivative]

Oh, right. It looked very intimidating at first, but I've got it figured out know. Thanks!