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Improper integrals

  1. Feb 24, 2014 #1
    1. The problem statement, all variables and given/known data

    integral of 1/sqrt(9-x^2)
    from 0 to 3

    2. Relevant equations


    3. The attempt at a solution
    I integrate it correct to arcsin(x/3) from 0 to 3
    Get the correct anwser of pi/2.

    But there is another question, At which value of x in the integration region [0,3] does special care need to be taken with the integration? I understand at some point it goes from negatie to positive, but i tried 0,3,pi/2,pi.. none worked.. anyhelp?
  2. jcsd
  3. Feb 24, 2014 #2


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    What did you get when you put ##x=3## into the integrand?

    And why do you say it goes from negative to positive?
  4. Feb 24, 2014 #3
    Check the domain of the original function to be integrated.
  5. Feb 24, 2014 #4
    I never had to do anything with the domain, it just worked.. But i guessed 0, pi/2 and 3. I thought it was be pi/2 because thats where it goes from neg to pos.
  6. Feb 24, 2014 #5
    That's because you have been doing "proper" integrals up to this point. Improper integrals involve integrating across a point where the function is not defined. In this case the the function is not defined at x = __. The normal procedure is to introduce a variable for that number and take the limit as a approaches that number.

    In this case, arcsin is defined on [0,1]. But the original function is not defined on [0,3].
  7. Feb 24, 2014 #6


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    Try answering my two questions.
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