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Homework Help: Help with integrals

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int[/tex] sin^-1y dy






    3. The attempt at a solution
    u=sin^-1y
    du=[tex]\frac{1}{\sqrt{1-y^2}}[/tex]
    v=y
    dv=dy

    [tex]\int udv=uv-[/tex] [tex]\int vdu[/tex]

    =ysin^-1y-[tex]\int \frac{y}{\sqrt{1-y^2}}[/tex]

    my main trouble is evaluating the integral at this point.
    I would appreciate it if someone could show me how to evaluate the integral
    [tex]\int \frac{y}{\sqrt{1-y^2}}[/tex]

    If it was [tex]\frac{1}{y}[/tex] then I can see it would be ln x
     
  2. jcsd
  3. Feb 2, 2009 #2

    Mark44

    Staff: Mentor

    Assuming the work leading to your last integral is correct (I didn't check), you can use an ordinary substitution, u = 1 - y^2, du = -2u du. It's pretty straightforward.
     
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