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Thread: indefinite integral

  1. #1
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    indefinite integral

    Evaluate the indefinite integral: ______________
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  2. #2
    Super Member Deadstar's Avatar
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    Let $\displaystyle x = \frac{7}{2}\sin(u)$ => $\displaystyle u = \arcsin(\tfrac{2}{7}x)$

    $\displaystyle dx = \frac{7}{2}\cos(u)$.

    Integral becomes...

    $\displaystyle \int \frac{(7/2)\cos(u)}{\sqrt{49 - 49\sin^2(u)}}du$

    $\displaystyle = \int \frac{(7/2)\cos(u)}{7\sqrt{1-\sin^2(u)}}du$

    $\displaystyle = \int \frac{(7/2)\cos(u)}{7\cos(u)}du$

    $\displaystyle = \int \frac{1}{2} du$

    $\displaystyle = \frac{u}{2}$.

    Substitute in $\displaystyle u = \arcsin(\tfrac{2}{7}x)$ to get...

    $\displaystyle \frac{1}{2}\arcsin(\tfrac{2}{7}x)$.

    Epic.
    Last edited by Deadstar; Apr 19th 2010 at 04:41 PM.
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