I took calculus about 2 semester ago, and I'm trying to brush up on polar coordinates. I integrated $-x^2+3$ from $x = -\sqrt{3}$ to $\sqrt{3}$ and I got $6.93$
Now I tried to convert it to polar coordinates, but I'm having trouble setting up the integral. This what I did.
$-x^2+3$ => polar coordinates => $-(r\cos\theta)^2+3$
then I did, $\int_0^{2\pi} \int_0^\sqrt{3} ( (-(r\cos(\theta))^2+3)r\space drd\theta$ and when I evaluate this I get a different answer than the Cartesian coordinate integral.
I also tried this $$\int_0^{2\pi} \int_0^{(-(r\cos\theta)^2+3)*r}1\space drd\theta = ?? $$
Any ideas? sorry about typing the integral, I don't know the syntax for laTex.
Thank you