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Integrating with respect to area? Past paper question

  1. Jan 24, 2017 #1
    • New member has been reminded to fill out the Homework Help Template in future schoolwork threads
    This isn't exactly homework or coursework, it is a past paper question that I cannot find a solution to (my university doesn't like releasing answers for some reason unknown to me).
    The question is attached as an image (edit: the image displays while editing but not in the post, so I'll try to type it out):

    uc?export=download&id=0B2XR9EE7g17JSFA5R3B6eTQ0LXc.png
    Question: Let A be the rectangle -2 ≤ x ≤ 2, -1 ≤ y ≤ 1. Evaluate ∫A x3 dA.

    I attempted to solve this by parametising x and y in terms of a new variable t, such that x = 2t and y = t for -1 ≤ t ≤ 1. Then I used the fact that A = xy to obtain A = xy = 2t2 and dA = 4t dt. Substituting into the integral with limits -1 and 1 gave my a final answer of 64/5, but I lack confidence in my method and answer.
    Should I use a double integral? Any help would be much appreciated.
     
  2. jcsd
  3. Jan 24, 2017 #2

    Mark44

    Staff: Mentor

    I don't see any reason NOT to use a double integral.

    BTW, what would you get from this integral? ##\int_{-1}^1 x^3 dx##
     
  4. Jan 24, 2017 #3
    Zero :)
    I think I understand it now, I tried a double integral method earlier and it gave me zero and I thought that it was wrong, but after considering it properly I think that it's right.
     
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