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Thread: Integration by Parts - definite integral

  1. September 2nd 2008, 06:42 PM #1
    symstar
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    Integration by Parts - definite integral

    Just evaluate the integral...
    \int_{0}^{1/2}\sin^{-1}{x} dx

    I used...
    u=\sin^{-1}{x}
    du=\frac{dx}{\sqrt {1-x^2}}
    dv=dx
    v=x

    The problem is that I get stuck with \int_{0}^{1/2}\frac{xdx}{\sqrt {1-x^2}} eventually and I'm not quite sure where to go with it. I thought of maybe doing a sub, but I'm not sure what to sub for.
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  2. September 2nd 2008, 06:46 PM #2
    Chop Suey
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    Substitute u = 1-x^2.
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  3. September 2nd 2008, 07:17 PM #3
    symstar
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    Subbing t=1-x^2

    \frac{1}{2} \sin^{-1}{\frac{1}{2}} + \int_{3/4}^{1} \frac{dt}{-2\sqrt{t}}

    Is this correct so far?
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