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Improper Integrals Question

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data
    I have to integrate this equation for my AP Calc BC class:

    2. Relevant equations
    I have to use the definition of an improper integral.

    3. The attempt at a solution
    I know that it is [tex]\arcsin(x)[/tex] from 0 to 1, and both are in the domain of the arcsin function, so i don't need to use the improper integral equation, and the answer is [tex]\frac{\pi}{2}[/tex]. But I find it weird that I'd be graded on a question that i don't need to use the topic for. Am I missing anything??
  2. jcsd
  3. Feb 2, 2009 #2


    Staff: Mentor

    Yes. The integrand isn't defined at x = 1, which makes it an improper integral. For this reason you need to use a limit to evaluate it. I.e.,
    \lim_{a \rightarrow 1^-} \int_0^a \frac{dx}{\sqrt{1 - x^2}}[/tex]
  4. Feb 2, 2009 #3
    oh. so it's the domain of the integrand. thanks :D
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