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Integration question

  1. Jun 22, 2011 #1
    1. The problem statement, all variables and given/known data

    [itex]\int_{-B}^{B}\frac{\sqrt{B^2 - y^2}}{1-y} dy[/itex]

    2. Relevant equations



    3. The attempt at a solution

    I tried to get rid of the square root thing, so I started by:

    [itex] y = B sin \theta, [/itex]
    [itex] dy = B cos \theta d\theta, [/itex]

    then the integral above becomes:

    [itex]B^2 \int_{0}^{\pi} \frac{\sin^2 \theta d\theta}{1-Bcos\theta}d\theta.[/itex]

    Now my question is, how to integrate this out?
     
  2. jcsd
  3. Jun 22, 2011 #2

    micromass

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    Hi deftist!

    The trick is to do the subtitution

    [tex]t=\tan(\theta /2)[/tex]

    and to apply the formula's

    [tex]\sin(\theta)=\frac{2t}{1+t^2},~~\cos(\theta)=\frac{1-t^2}{1+t^2},~~\tan(\theta)=\frac{2t}{1-t^2}[/tex]
     
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