Set up an integral for the ∫∫xydA for the region bounded by y=x, y=2x-2, and y=0. Set up the dxdy integral, then the dydx integral, then evaluate the simplest of the two.
The Attempt at a Solution
I drew the region which was easy enough, and the easier integral to come up with was the dxdy integral with the y bounds from 0 to 2 and x from y to (y+2)/2. I'm pretty positive this one is correct, but my troubles show up when I try to come up with one for dydx. I know the x boundary is 0 to 2 but the y boundary is confusing me. I first tried from 2x-2 to x but that didn't give me the same answer as the dxdy integral. Then I tried a y boundary from 0 to x and that didn't work either. Any hints at what is giving me problems would be appreciated.