FibonacciMariachi 3 years ago 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)

1. TuringTest

so, where are you stuck?

2. FibonacciMariachi

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.

3. FibonacciMariachi

I do have the right answer if you want it.

4. TuringTest

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

5. FibonacciMariachi

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

6. TuringTest

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

7. FibonacciMariachi

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

8. TuringTest

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

9. FibonacciMariachi

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

10. TuringTest

good luck!

11. FibonacciMariachi

thanks