00:01
Okay, we want to integrate this function to x minus y over the region where r is the region in quadrant one enclosed by the circle x squared plus y squared equals four.
00:15
There it is.
00:17
And the lines x equals zero and y equals x.
00:26
Okay, so then only place touched by all three is this piece right here pie piece.
00:34
Okay, so we'll look at a little section here.
00:38
So it's starting here.
00:38
At r equals zero and going out here to r equals two okay theta starting at the line y equals x well the place where y equals x that's theta equals pi over four and then going to here pi over two okay two x minus y that will be two r cosine theta plus oops minus two 1 r sign theta and then remember da is r d -d -theta okay so we have pi over 4 to pi over 2 0 to 2 then go ahead and factor the r out here r times 2 cosine theta minus sine theta oh and this are also r squared d r d theta i'll need that parenthesis there okay the r comes from the first one is this one that's factored out times this one.
02:07
Okay, it looked like it's going to be really hard, but it's not very hard at all now that i've got it all set up.
02:12
It's pi over four to pi over two.
02:17
Integral of r squared d r is r cubed over three from zero to two...