Polar Coordinates problem
Posted on 2003-11-22
I have a question on a homework assignment that says I have to evaluate a given integral by converting to polar coordinates. It gives us a sum of two integrals that we can combine into 1 integral by converting to polar coordinates. Im not having trouble getting down to one integral, but my issue is when i actually try to integrate. I know x = rcos(theta) and y = rsin(theta). The function was f(x,y) = xy. So then when I convert to polar coordinates, it becomes the double integral of (rsin(theta)) * (rcos(theta) r dr d theta right? I don't need help with the limits of integration, thats why I am not including them. So I integrate with respect to r first, and get (r^4/4)*(sin(theta) * cos(theta)), for some interval values, dtheta. Evaluate that integral with the appropriate interval values, then I try to integrate with respect to theta now, and I end up with the integral of sin(theta) * cos(theta) dtheta, and I don't know how to integrate this :( I think I set it up right, but I'm confused to how to integrate sin(theta)*cos(theta).
I hope I explained this clearly enough....
Thanks in advance,