# Integrating a circle

1. Apr 20, 2010

### julian92

1. The problem statement, all variables and given/known data

integrating a circle ,,
my main question is that, can we integrate it by contour integration technique ?
and if yes ,, would you plz show me how :) or just give me a hint :D

2. Relevant equations

y^2 + x^2 = a^2

where a= r

suppose that a = 2

3. The attempt at a solution

i know that it can be done as two semicircles
taking a substitution x=2sin(u) ,, or even by integration by parts!!!

Last edited: Apr 20, 2010
2. Apr 20, 2010

### justsof

integrating a circle = integrating to find the surface of a circle?
You should check out Green's theorem, it connects line/contour integration in 2D with surface integration.

3. Apr 21, 2010

### julian92

well ,, the thing is that i'm not really good at contour integration ,, i've been searching for a text to study contour integration for ages ,, and still can't find one with good details and examples

and still don't know when to use contour integration!!

and since circles can't be integrated using the normal integration techniques ,, i wondered if it could be done using contour!!

and i got stuck at this problem ,, and really want to integrate that little circle :(

4. Apr 21, 2010

### HallsofIvy

What do you mean by "integrating a circle"? Integrating a function of two variables over the surface of a circle? Integrating around the circumference of a circle?

5. Apr 21, 2010

### julian92

I'm really not sure about the difference of the two :S

Does each one have a different method of integration?