Unit Circle?

[mudifier]

So, I have a calculus question on hand about double integrals and volume.  It's a practice problem without any solution, so I was wondering if people could give input

Comments

[chamcha]

You want to integrate 2xy over the first quadrant of the unit circle.
We start by noticing that
x = rcosQ,
y = rsinQ.
So to integrate over the unit circle, we integrate from Q = 0 to Q = pi/2 and the radius goes from r = 0 to r = 1.
Then, what we integrate is...
2r^2cosQsinQ*r drdQ. Be sure to remember the Jacobian r that goes with dQ.

[mudifier]

We couldn't do this using cartesian coordinates?

Because I have double integrals from 0-1, 0-sqrt(1-x^2) of 2xy dydx.

I ended up with 1/4units cubed.

That can't be right

[chamcha]

Yep you can do it that way, too. I just like polar coordinates.

And why can't 1/4 units cubed be right? ;)