# Homework Help: Integral along a closed loop

1. Apr 19, 2006

### rocket

i want to prove that this integral along a closed loop:

$$\oint (1/r^2) dr$$

is equal to zero. but i'm not sure how to prove it. i was wondering if someone can show me a rigid proof for this. I think i'm missing something here because I'm not really that familiar with loop integrals.

2. Apr 20, 2006

### e(ho0n3

Pick two points, A and B, and two curves, C_1 and C_2 where C_1 goes from A to B and C_2 from B to A.

Now calculate the line integral along the curve C_1 and C_2. They should both be equal, in which case, the loop integral will be 0.

3. Apr 20, 2006

### Hash

Since $$1/\tau^2$$ is an analytic function with a singularity in 0 (a pole of order 2), the contour your want to use is closed, then you can use the Cauchy's theorem on residues.

$$\oint 1/\tau^2 \, d\tau = 2i\pi \cdot 0$$

where 0 is the residue of $$1/\tau^2$$