00:01
In this problem, we are looking at to evaluate the double integral over a region r of x squared da.
00:11
But here r is bounded by the ellipse whose equation is 9x squared plus 4 y squared equals to 36.
00:29
And we are using the change of variables where x is now going to equal to 2 u and y is equal to 3v so we compute the jacovian first to start off and the jacovian is partial x comma y or partial u comma v which in this case is a determinant of partial x partial u partial x partial b partial partial partial partial partial u, partial, partial, v, and here is y.
01:03
So pretty much these would be equal to the determinant of the matrix that we have here, in this case, partial x, partial u, that's going to be 2.
01:13
Partial x, partial v is 0, partial y, partial u is 0, partial y partial u is 0, partial y partial v is 3.
01:21
So in this case, the determinant is simply the product of 2 and 3, which is 6 in this case.
01:29
Note, the next thing that we have here is that r is bounded by the ellipse that we have here is 9 x squared plus 4 y squared which is 36.
01:38
Well, we can write this down as 3.
01:43
Yeah, we can write this out by dividing everything by 9...