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Homework Help: Evaluate the integral by interpreting it in terms of areas

  1. Jul 19, 2010 #1
    1. The problem statement, all variables and given/known data

    The problem is in the attachment along with my answer. Can please one check if I got a correct answer?
    Some sources say the answer is 2Pi instead of just Pi.


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Jul 19, 2010 #2

    Char. Limit

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    Gold Member

    I'm not sure where you got that your graph was a quarter circle. The shape is right, but you need to check your bounds...
     
  4. Jul 19, 2010 #3
    That is because x cannot be less than 0. In the problem, we take a square root of it, so x is more or equal to 0.
    Right?
     
  5. Jul 19, 2010 #4

    Char. Limit

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    Gold Member

    No, x can be less than zero. Your definite integral is from -2<x<2, after all. What is under your square root is not x, but 4-x^2. So 4-x^2 has to be greater than or equal to zero. Follow?
     
  6. Jul 19, 2010 #5
    Please take look at a sample question in my book. I did my problem based on this example. I think I followed all its steps.
     

    Attached Files:

  7. Jul 19, 2010 #6
    As Char limit has pointed out, they are similar in the fact that they deal with the graph of a circle, but check the bounds of the example problem and compare those with your problem, now think about how they differ.

    Joe
     
  8. Jul 19, 2010 #7
    Now I see, I didn't know that I should consider the bounds. Thank you, I got it.
     
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