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Homework Help: Tricky Integration

  1. Jun 24, 2010 #1
    1. The problem statement, all variables and given/known data


    [tex]E = \frac{e^2}{4 \pi \epsilon_0 a_0^3 } \left( - b \int_0^b e^{- \frac{2r}{a_0}} dr + \int_0^b r e^{- \frac{2r}{a_0}} dr \right)[/tex]

    I have to use these integrals,

    [tex] \int_0^x e^{-u} du = 1 - e^{-x}[/tex] and [tex] \int_0^x u e^{-u} du = 1 - e^{-x} - xe^{-x}[/tex]

    I get:





    3. The attempt at a solution

    [tex]E = \frac{e^2}{4 \pi \epsilon_0 a_0^3 } \left( - \frac{a_0 b}{2} (1 - e^{- \frac{2b}{a_0}}) + \left(- \frac{- a_0 b}{2} e^{- \frac{2b}{a_0}} - \frac{a_0^2}{4} e^{- \frac{2b}{a_0}} + \frac{a_0^2}{4} \right) \right) [/tex]
     
  2. jcsd
  3. Jun 24, 2010 #2

    phyzguy

    User Avatar
    Science Advisor

    I think you blew a sign in the third term. It should be negative, not positive. Otherwise, it looks correct.
     
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