anonymous
  • anonymous
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)
Mathematics
chestercat
  • chestercat
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TuringTest
  • TuringTest
so, where are you stuck?
anonymous
  • anonymous
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
  • anonymous
I do have the right answer if you want it.

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TuringTest
  • TuringTest
your steps are fine, but I would just convert the lines to u and v instead of the "critical xy points"
anonymous
  • anonymous
oh? How would I do that? That sounds a lot easier.
TuringTest
  • TuringTest
just sub in x=1/5(3u+v), y=1/5(v-2u) into each equation for the boundary of R
anonymous
  • anonymous
Ohhhh, alright. So once I converted to uv form would I just replot the graphs and look for my bounds?
TuringTest
  • TuringTest
yeah, it will most likely be a square in the u v plane
anonymous
  • anonymous
Gotcha, Ill rework the problem. That sounds a lot better than just looking for the points which takes forever.
TuringTest
  • TuringTest
good luck!
anonymous
  • anonymous
thanks

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