# The Cauchy Integral Formula

## Homework Statement

Use Cauchy's integral formula to evaluate
when
a) C is the unit circle
b) c is the circle mod(Z)=2

## Homework Equations

I know the integral formula is

## The Attempt at a Solution

for the unit circle I was attempting F(z)=sin(z) and Z0=∏/2, which would give a solution of 2∏i, however if this is the correct method I am unsure how to modify it for a larger unit circle as I thought the final result was independent of radius

Office_Shredder
Staff Emeritus
Gold Member
The integral formula requires the point z0 to be contained inside of the curve gamma that you are integrating around. Draw some pictures and you should see the difference between the two curves they are asking you to integrate on

Ah so the unit circle wouldn't actually contain the point pi/2 whereas the circle mod(z)=2 would?

Office_Shredder
Staff Emeritus
Gold Member
That's right. So in the unit circle case you need to figure out something else that lets you calculate the integral

Can I then use the integral theorem that says it will equal 0?

Office_Shredder
Staff Emeritus