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Integral of Square Root of Sin(x)

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the Integral of [tex]\sqrt{sin(x)}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    People say it's -2/3cos(x)[tex]^{3/2}[/tex]
    which I dont think so or is it?

    thank you
  2. jcsd
  3. Jan 26, 2010 #2


    Staff: Mentor

    [tex]\int \sqrt{sin(x)} dx = \int sin^{1/2}(x) dx[/tex]

    The people you mention are using the formula
    [tex]\int u^{1/2} du = \frac{2}{3}u^{3/2} + C[/tex]
    but are doing so incorrectly.

    In the problem you gave, u = sin(x), but du = cos(x)dx, which is not present, so the formula I gave above is not applicable.
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