integration around a circle

[hgd7833]

How to integrate f(x) = lnx on the circle (x-a)^2 + (y-b)^2 = R^2 ???

 

I will have ti use complex analysis

 

 

 

 

 

 

 

 

Thank you

 

 

 

 

 

 

 

 

 

 

 

[Cap'n Refsmmat]

I'm not sure I understand the question. Your function is a function of x only, yet you're integrating it over a circle in x and y. Is that intended?

 

How much complex analysis do you know? There are many ways to approach an integral in complex analysis. If you could tell us what you've tried and what problems you've encountered, we could help you much more easily. I don't know whether to suggest residues, direct integration, or some other creative method.

[hgd7833]

I am sorry, the function is a function of r, so f® = lnr , and i was trying to change in polar coordinates, r = (x^2 + y^2)^1/2 , and double integral

but i couldn't do it

[Cap'n Refsmmat]

Where is ln® analytic? r is always real and non-negative, so you should be able to deduce something about the analyticity of the function. And that may tell you something helpful about the value of the integral.

 

It would be helpful if you describe what problems you encounter, rather than just saying you couldn't get the answer.

[hgd7833]

Hi Cap'n Refsmmat

 

 

 

Actually the problem is:

 

Find the mean value of the function ln(r ) on the circle (x-a)^2 + (y-b)^2 = R^2