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Evaluate the integral by interpreting it in terms of areas.

  1. Dec 2, 2012 #1
    1. The problem statement, all variables and given/known data

    from [-2,2] rad(4-x^2)

    2. Relevant equations



    3. The attempt at a solution
    I know its a circle and i get the equation to be y^2+x^2=4

    and I believe it has to be divided into a circle and rectangle
    so the area of the rectangle i got to be 2
    the circle i got to be 1/2(since its a half circle) times ∏(2)^2
    the answer i got is
    2+2pi (which is wrong) dont know where I went wrong tho.
     
  2. jcsd
  3. Dec 2, 2012 #2

    Curious3141

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    Where did the rectangle come from? It's just a semicircular area.
     
  4. Dec 2, 2012 #3
    I was doing a simliar problem of [-5,0] where it was evaluating 1+rad(25-x^2) dx
    And the solution had a the area broken up into a rectangle and a semicircle
    I guess i tried to apply the same technique to this problem.
    The answer came out to be 5+(25pi)/4
     
  5. Dec 2, 2012 #4

    haruspex

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    The 1+ gave the rectangle there. You have no corresponding term here. Did you sketch the curve? Do you see a rectangle when you do?
     
  6. Dec 2, 2012 #5

    Mark44

    Staff: Mentor

    When you're using what you found in a "similar" problem, make sure it's actually similar to the one you're working on.

    As suggested by others in this thread, a quick sketch of the graph of x2 + y2 = 4 would show that your region is just the upper half of a circle.

    Sketching a graph is usually the first thing you need to do in these problems.
     
  7. Dec 3, 2012 #6
    Thanks for the advice/ help
     
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