Evaluate the integral by using the following transformation:

∫∫(R) x*y^2 dA, where R is the region bounded by the lines x-y=2, x-y=-1, 2x+3y=1, and 2x+3y=0; let x=1/5(3u+v), y=1/5(v-2u)

Question

Evaluate the integral by using the following transformation:

∫∫(R) x*y^2 dA, where R is the region bounded by the lines x-y=2, x-y=-1, 2x+3y=1, and 2x+3y=0; let x=1/5(3u+v), y=1/5(v-2u)

turingtest · Answer

so, where are you stuck?

anonymous · Answer

Well, I tried doing the problem and I didn't get the right answer. Are these the correct steps to get to the answer?

1. Plot x/y coordinate graph.
2. Convert critical xy points to uv points.
3. find the Jacobian.
4. Set up the integral in terms of u and v with the jacobian.

anonymous · Answer

I do have the right answer if you want it.

turingtest · Answer

your steps are fine, but I would just convert the lines to u and v  instead of the "critical xy points"

anonymous · Answer

oh? How would I do that? That sounds a lot easier.

turingtest · Answer

just sub in x=1/5(3u+v), y=1/5(v-2u) into each equation for the boundary of R

anonymous · Answer

Ohhhh, alright. So once I converted to uv form would I just replot the graphs and look for my bounds?

turingtest · Answer

yeah, it will most likely be a square in the u v plane

anonymous · Answer

Gotcha, Ill rework the problem. That sounds a lot better than just looking for the points which takes forever.

turingtest · Answer

good luck!

anonymous · Answer

thanks