Question

Evaluate the double integral and sketch the region R.

Answer 1

\[\int\limits_{0}^{\pi/2}\int\limits_{0}^{1\sin \Theta}\Theta r dr d \theta\]

Answer 2

^ This involves change of variables with polar coordinates

Answer 3

The limits for theta are 0 to pi/2. The limits for r depend on theta. They always start at 0 and go to sin(theta)

Answer 4

I integrated the problem correctly with respect to dr, but dtheta is where I'm stuck at

Answer 5

sin(0) is 0. sin(pi/2) is 1, so as theta increases, the upper limit for r goes from 0 to 1.

Answer 6

This is how far I got:

\[\int\limits_{0}^{\pi/2} \theta r^2/2 d \theta\]