Integrating a Circle: Contour Integration Technique

[julian92]

Homework Statement

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

Thanks is advance :-)

Homework Equations

y^2 + x^2 = a^2

where a= r

suppose that a = 2

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!

 

[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.

 

[julian92]

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.

thanx for the reply
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 :(

 

[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?

 

[julian92]

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?

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

Does each one have a different method of integration?

Thanks in advance :)