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Integration by Parts of <C> i just cannot do

  1. Jun 4, 2005 #1
    Can anyone outline, and this is a rather large request, the step by step integration by parts for <C>? This is not a homework question but more something i need to be able to do on tuesday for my final, and have been trying to do for two days.

    Attached Files:

  2. jcsd
  3. Jun 4, 2005 #2


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    Homework Helper

    Your answer is incorrect.

    Here's how it's done.

    Knowing this integral's value

    [tex] I'_{1}(\alpha)=:\int_{0}^{+\infty} C e^{-\alpha C^{2}} \ dC =\frac{1}{2\alpha} [/tex] (1)

    ,one sees immediately that

    [tex] I'_{3}(\alpha)=:\int_{0}^{+\infty} C^{3} e^{-\alpha C^{2}} \ dC=-\frac{d}{d\alpha}I'_{1}=\frac{1}{2\alpha^{2}} [/tex] (2)

    and now plug in (2) the expression for '\alpha'.

  4. Jun 4, 2005 #3
    Thank you, and you're right, i forgot to type the pi in the denominator for the answer.
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