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Can't understand this integral!

  1. Aug 6, 2009 #1
    http://www.ph.qmul.ac.uk/phy108/CM2005_week2_Lecture3_Interatomic%20Forces2.pdf [Broken]

    Take a look at page 4 example 1.

    Why is it, when he performs the integral, it's n-1? What happens when he puts the limts in? Where is the infinty?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 6, 2009 #2

    Mark44

    Staff: Mentor

    First question: It looks like a mistake to me. The basic integral is
    [tex]-A\int \frac{1}{x^n} dx = -A \int x^{-n} dx = \frac{-A}{-n + 1}x^{-n + 1} + C[/tex]
    If you take the (-1) from A and multiply the (-n + 1) you get (n - 1). The exponent of n on the 1/r' is incorrect.

    Second question. For the infinite integration limit you need to substitute a noninfinite variable in for r', and then let that variable get larger without bound.
     
    Last edited by a moderator: May 4, 2017
  4. Aug 6, 2009 #3
    Thanks for that.

    So what happens (result) when he subtracted this ever increasing value of r?

    Also, how do you multiply the -1 to the power? (well I know how, but I wouldn't have thought I could do that?)
     
  5. Aug 6, 2009 #4
    Actually, it is correct, because his answer is in terms of (1/r). Using your example, you have x^(-n+1). By turning x to 1/x, you introduce another negative sign on the exponent making it
    x^(n-1)

    Edit: That last part, that I wrote, should be (1/x)^(n-1).
     
  6. Aug 6, 2009 #5

    Mark44

    Staff: Mentor

    The final answer might be correct (I haven't finished the problem), but the expression he (she?) got for the antiderivative is incorrect for the reason I gave in my previous post. That is, unless you can convince me that my work is in error.
     
  7. Aug 6, 2009 #6
    Oh..you mean the part on the second line all the way on the right side...yeah, looks like a typo on the first r' term in the denominator, should be -n+1. I was looking at the final line, which is correct.
     
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