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Homework Help: Double integral limits?

  1. Jan 21, 2014 #1
    1. The problem statement, all variables and given/known data

    ∫∫ydxdy over the triangle with vertices (-1,0), (0,2), (2,0)

    2. Relevant equations

    I did it like this and got the right answer:

    ∫dy ∫ydx

    this first:
    ∫ydx from x = (y-2)/2 to x = 2-y

    then ∫dy from y = 0 to y = 2

    I got 2 which is correct

    but when I tried another method, splitting them up across the y axis i got 8/3:

    I did I = A+B

    A = ∫dx∫ydy

    ∫ydy from y = 0 to y = 2x+2

    then I integrated from x = -1 to x =0 (I got 2/3)

    B = ∫dx∫ydy

    ∫ydy from y =0 to y = -x+2

    then I integrated wrt x from x = 0 to x = 2 (I got 2)

    so the second answer was 8/3

    Why was the second one wrong? I keep getting questions wrong because of the limits I choose! Could someone help me out please?

    3. The attempt at a solution
  2. jcsd
  3. Jan 21, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your limits look to be correct with both methods. Without you showing your calculations instead of just giving us your answers, we can't tell where your mistake is.
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