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Solve this integral

  1. Jun 16, 2004 #1

    jcsd

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    Can someone solve this integral as the answer I get looks suspicously complicated:

    [tex]\int^{0}_{\frac{-u}{a}} t\sqrt{1 - \frac{(u + at)^2}{c^2}} dt [/tex]
     
  2. jcsd
  3. Jun 16, 2004 #2

    AKG

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    Make the substitution [itex]\frac{u + at}{c} = \cos \theta[/itex]. You should be able to get it down to this:

    [tex]\frac{c}{a^2} \left (u\int _{\frac{\pi}{2}} ^{\arccos \left(\frac{u}{c}\right)} \sin ^2 \theta d\theta - c\int _{\frac{\pi}{2}} ^{\arccos \left(\frac{u}{c}\right)} \sin ^2 \theta \cos \theta d\theta \right )[/tex]

    And you can easily solve that on your own.

    EDITED to fix limits of integration as per HallsOfIvy's comment.
     
    Last edited: Jun 16, 2004
  4. Jun 16, 2004 #3

    HallsofIvy

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    The substitution might work but the limits of integration are wrong. When t= 0, cos[theta]= u/c so [theta]= cos<sup>-1</sup>(u/c). When t= u/c, cos[theta]= 0 so [theta]= [pi]/2.
     
  5. Jun 17, 2004 #4

    jcsd

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    Thanks for that, I realized I made a slight error so it became slightly easier to solve.
     
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