Math Help - General multiple integration question

1. General multiple integration question

Ok there's something simple I don't get here. When one double integrates a circle in polar coordinates or even cylindrical coordinates, sometimes one subs in x=rcostheta and y=rsintheta but sometimes x=3costheta and y=3sintheta even when we know both times that the radius of he circle is 3. Can anyone tell me how one knows when to plug in the radius and when just to leave it as r? I just got a question wrong because I put r instead of 3...

2. Originally Posted by Zirtco
Ok there's something simple I don't get here. When one double integrates a circle in polar coordinates or even cylindrical coordinates, sometimes one subs in x=rcostheta and y=rsintheta but sometimes x=3costheta and y=3sintheta even when we know both times that the radius of he circle is 3. Can anyone tell me how one knows when to plug in the radius and when just to leave it as r? I just got a question wrong because I put r instead of 3...
If you leave the radius as r then then this solves for the general case. You can then substitute 3 for r at the end and find out the result. One advantage of this is that if then you had to solve the same problem with radius 2 you could simply substitute 2 for r and the work would be less.

If that doesn't solve it then perhaps you should tell us what the question was that you got wrong?

3. Re:

No idea why the cross product was required. There's another way to do it isn't there? There's the solution to part a as well.