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Double Integration - Finding the limits

  1. Nov 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the limits of the integral of z = f(x,y) over the region bounded by the x-axis, and the semi-circle x2 + y2 = 4, y ≥ 0

    2. Relevant equations

    3. The attempt at a solution

    Where do I start on this question? I can't understand what it is asking.


    Am I supposed to find a,b,c,d limits of the double integrals? If so, can you please point me in the right direction. I am completely lost.
  2. jcsd
  3. Nov 5, 2008 #2


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    Staff Emeritus
    Science Advisor

    It seems simple enought to me. x2+ y2= 4 gives a circle with center at (0, 0) and radius 4. You are asked to integrate over the top half of that: y> 0.

    Since the problem specifically said "find the limitsof integration", yes, that is what you are supposed to do! I recommend that you start by drawing the graph.

    Remember that, since the final result is a number, the limits of integration on outer integral must be numbers. It will be simplest to integrate over y first then x so the limits of integration must be values of x. What is the smallest x value in this region? That will be the lower limit. What is the largest x value in this region? That will be the upper limit.

    The "inner" integral is with respect to y so the limits may be functions of x. Draw a vertical line on your graph representing some value of x. What is the y value of the lower end of that line? That is the lower limit on the integral. What is the y value on the upper end of that line (a function of x)? That is the upper limit on the integral.
  4. Nov 5, 2008 #3
    Ok that is much more clear now. Thank you.
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