(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let C denote the positively oriented boundary of the square whos sides lie on the lines (x= + / - 2 and y = + / - 2)

Evaluate int_c (e^(-z) dz) / (z - (pi*i/2))

The answer is simply 2*pi

2. Relevant equations

This is a text book question after the topic of Cauchy Integrals but before residues

3. The attempt at a solution

I am not very cluely at the Contour integration as the teacher just gave us the text book notes and said do it... so I figure to use the Cauchy Integral

f(z_0) = 1/(2*pi*i) int_c f(z) dz / z - z_0

Where my belief is that z_0 is interior to the given contour (in this case it's the square)

so I thought that the question looks like it will just fit inside the formula, so to speak, because (pi*i)/2 is interor to the contour (well if it's not then I have no idea what i'm talking about) so then i put

f(z_0) = 1/(2*pi*i) int_c e^z dz/ z - ((Pi*i) / 2)

so I sub in f(z_0) = e^(Pi*i) and get -1

so -1 = 1/(2*pi*i) int_c e^z dz/ z - ((Pi*i) / 2)

-2*pi*i = int_c e^z dz/ z - ((Pi*i) / 2)

and thats where I stop :surprised because I dont know how to integrate e^z dz/ z - ((Pi*i) / 2)

Any suggestions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integral of e^(-z) dz / (z - (pi*i)/2)

**Physics Forums | Science Articles, Homework Help, Discussion**