Question

The double integral of f=(x^2+y^2), x from -1 to 2 and y from 0 to sqrt(4-x^2). I need to do this with integration in polar coordinates but I have no idea how to express the cutoff at x=-1. Help!

Answer 1

draw it.

Answer 2

split into two integrals here.

Answer 3

\[
x=-1 \implies r\cos\theta = -1 \implies r=-\sec\theta
\]

Answer 4

Is it absolutely necessary to split this in to 2 integrals? If so then I know what I'm doing wrong. Is there a way to solve it using a single double integral?

Answer 5

You must split it up.

Answer 6

I see. Thanks for your help!

Answer 7

You have two \(r(\theta)\) function and I see no way of combining them nicely.