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Double integral, change of variables or no

  1. Oct 1, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫∫Se2x+3ydydx where S is the region |2x|+|3y|≤ 1

    2. Relevant equations



    3. The attempt at a solution

    So I've done this two ways and gotten two different answers and I'm not sure which is right. I used change of variables where where u=3y+2x and v=3y-2x and I got an answer of 24(e-1/e) with a jacobian of 12 and my bounds from -1 to 1 for both u and v. Then I did it in x, y coordinates and I got 4 times the given integral from x=0 to 1/2 and y=0 to (1-2x)/3 and I got a final answer of 2/3, please help me know which one is right!?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 1, 2012 #2

    SammyS

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    e3y+2x is neither symmetric in x nor y, so you can't take 4 times the integral over 1/4 the region.
     
  4. Oct 1, 2012 #3
    So would the answer be 24(e-1/e) or is that wrong?
     
  5. Oct 1, 2012 #4

    SammyS

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    The integrand does not have the proper symmetry to do any such short cut.

    You need to integrate of all of region S.
     
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