Use the ML inequality right? If on the contour and the length of the contour is L then:
On the unit circle , . Therefore .
I have a problem:
Let gamma: z=e^(it) (0<= t <= pi). Show that
|integral (e^z / z) dz | <= pi e^2
I thought to use the Estimation theorem:
But at the end of |f(gamma(t))| i found e^(2cost)/2
And at the end of |(gamma'(t)| i founf 2.
But i don't understand how can i integrate e^(2cost)