- #1
mcafej
- 17
- 0
Homework Statement
Consider the change of variables x = x(u, v) = uv and y = y(u, v) =u^3+v^3
Compute the area of the part of the x-y plane that is the transform of the unit square in the
2nd quadrant of the u-v plane, which has one corner at the origin. (Since the transformation
is 1:1 on the second quadrant (assignment 6), the area equals the integral over the square of
the absolute value of the determinant of the Jacobian of the transformation.)
The Attempt at a Solution
So I computed the Jacobian to be 3v^3-3u^3. Then, since I just needed to integrate over a square, I did
∫[itex]^{1}_{0}[/itex]∫[itex]^{0}_{-1}[/itex] 3v[itex]^{3}[/itex]-3u[itex]^{3}[/itex] du dv. I keep getting 0 as an answer, but that just doesn't seem right, am I misunderstanding the question?
also, sorry if my formatting is confusing, I don't really know how to make the integrals look pretty