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Homework Help: Double integral with absolute value

  1. Jul 15, 2016 #1
    1. The problem statement, all variables and given/known data

    I am trying to evaluate double integral
    ∫∫D (|y - x2|)½

    D: -1<x<1, 0<y<2

    2. Relevant equations


    3. The attempt at a solution

    I know that in order to integrate with the absolute value I have to split the integral into two parts:

    I just can't get of the limits of the integral

    (it is this same questions https://www.physicsforums.com/threads/absolute-value-in-a-double-integral.202157/ )

    Please I been trying to set this up for hours how
    Last edited by a moderator: Jul 15, 2016
  2. jcsd
  3. Jul 15, 2016 #2


    Staff: Mentor

    You've written the same thing twice. If y > x2, then |y - x2| = y - x2.
    If y < x2, then |y - x2| = -(y - x2) = x2 - y.
    Region D is just a rectangle.
  4. Jul 17, 2016 #3
    I forgot the function |y - x^2| is inside a square root. When I divide the two integrals for y > x2, |y - x2| = y - x2.
    and y < x2, |y - x2| = -(y - x2) = x2 - y. I really dont know what would be the limits of integration would it be -1 to what then the other other what to 1?
  5. Jul 17, 2016 #4

    Charles Link

    User Avatar
    Homework Helper
    Gold Member

    It takes a little practice to figure out how to select the limits of a double integral. If you choose to do the dy integral first, for each location x, the dy integral is performed and you need to figure out the limits (that often depend on x.). Then the dx integral is done adding up all the strips that were solved individually (as a function of x) when you did the dy integral.
  6. Jul 17, 2016 #5
    Thanks I think I got it!
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