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Reduction formula/Integration by parts problem

  1. Sep 1, 2007 #1
    1. The problem statement, all variables and given/known data
    The problem asks me to: Determine a reduction formula for the stated integral (See Picture and problem at:

    http://garciarussellchem.angelfire.com/Photo/

    [​IMG]
    Please help me out with this problem. I don't understand why they do not include an extra r in the denominator when integrating dv. I also don't understand what purpose the r^(n-1) serves.

    This is a bit confusing.

    Thank you.
     
    Last edited: Sep 1, 2007
  2. jcsd
  3. Sep 1, 2007 #2

    learningphysics

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    Homework Helper

    They are using [tex]u = r^{n-1}[/tex] and [tex]dv = re^{-ar^2}dr[/tex] then doing integration by parts with those...
     
  4. Sep 1, 2007 #3
    This means that v must equal"

    v= (re^-(ar^2))/-2ar in order for us to get the dv back right?

    THANK YOU FOR THE QUICK REPLY :) !
     
  5. Sep 1, 2007 #4

    learningphysics

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    No prob.

    If you differentiate [tex]\frac{-1}{2a}e^{-ar^2}[/tex] you get [tex]re^{-ar^2}[/tex], so that's why [tex]v = \frac{-1}{2a}e^{-ar^2}[/tex]
     
  6. Sep 1, 2007 #5
    Thanks a bunch.
    This site rocks.

    (thank you)^(10)
     
    Last edited: Sep 1, 2007
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