Can't understand this integral

[Lavace]

http://www.ph.qmul.ac.uk/phy108/CM2005_week2_Lecture3_Interatomic%20Forces2.pdf

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?

 

[Mark44]

http://www.ph.qmul.ac.uk/phy108/CM2005_week2_Lecture3_Interatomic%20Forces2.pdf

Take a look at page 4 example 1.

Why is it, when he performs the integral, it's n-1?

First question: It looks like a mistake to me. The basic integral is
$$-A\int \frac{1}{x^n} dx = -A \int x^{-n} dx = \frac{-A}{-n + 1}x^{-n + 1} + C$$
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.

What happens when he puts the limts in? Where is the infinty?

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.

 

[Lavace]

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?)

 

[Chrisas]

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).

 

[Mark44]

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).

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.

 

[Chrisas]

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.