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Homework Help: Solve Integration

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Please prove the integral in the attachment

    2. Relevant equations

    3. The attempt at a solution
    Tried many ways to solve it. Integration by parts, trig sub etc.
    The closest one is the substitution $U=\frac{r^2}{2}-\frac{R^2/2}+x^2$, which gives some arcsin. I change it into arctan, but it is not the arctan mathematica shows. I guess it has something to do with the $\sqrt{R^2 - x^2}$, since it will blow up at R. May need delta function to handle it.

    Attached Files:

    Last edited: Jan 24, 2013
  2. jcsd
  3. Jan 24, 2013 #2

    Simon Bridge

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    Welcome to PF;
    Nice try :)
    This is your homework - we can help you where you get stuck but you have to do the work.

    Please give it a go and show your working as far as you get.
    Try to describe how you are thinking about the problem as you go.
    Don't worry about looking stupid - we've all done this before: you are among understanding, and friendly, people here.
  4. Jan 25, 2013 #3


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    You tried many ways- please show us at least some. If possible one where you feel you came closest to solving the problem. That will make it easier to give suggestions.
  5. Jan 25, 2013 #4

    Simon Bridge

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    Well your integral (off the supplied attachment) seems to be: $$\int_0^b \frac{x.dx}{\sqrt{a^2+x^2}\sqrt{b^2-x^2}}=\frac{a\arctan(b/a)}{\sqrt{a^2}}$$ ... since there is no ##r## or ##R## in the integrand, it is difficult to see your reasoning behind the substitution. From context - I'm guessing R=b and r=a?

    Considering the arctan in the solution - perhaps a substitution like ##x=a\tan\theta## and a table of trig identities will be the way to go?
    Did you try that?

    However, HallofIvy is right - it is better for you to go step-by-step through the one you felt got the closest.
    So you made the substitution: what was the next step?

    (I know: it's a pain typing out the math. Use the "quote" button off the bottom of this post and see how I was able to type the math out ... you can copy and paste then make minor adjustments.)
    Last edited: Jan 25, 2013
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