You see that we're "walking" counter-clockwise - thus we should have . There would be a negative signal if we walked clockwise.
Well. We should determine the limits of integration. I mentioned above the convenience because this integral is asking so much that we change it for polar coordinates - therefore we can easily find the limits of integration (I think the sketch speaks by itself). So we put:
Our angle will vary from 0 to and the radius will vary from 0 to 1 (unit circle). This will lead us to:
Ah, before, we can't forget the Jacobian (I will not show this, but you should know how its done), so . Finally, the integral becomes:
because by our change.
Jul 28th 2010, 09:33 PM
It says counter-clockwise in the question!
Jul 28th 2010, 09:39 PM
Oh, my mistake, sorry. I'll correct it.
Jul 28th 2010, 09:44 PM
Thank you so much for the quick replies. I appreciate it a looooot! I will try it out and see what I can come up with. And keep you guys updated.