Evaluate the contour integral of z^2/(4-z^2) around the circle |z+1|=2.
The question is attached in correct mathematical notation, along with the student's (incorrect) initial attempt. You will need to refer to this initial attempt when reading the solution.
Cauchy's formula can be used to quickly evaluate contour integrals of complex valued functions. The solution comprises approximately one page written in Word with equations in Mathtype illustrating one example. The general procedure for these questions often involves decomposing into partial fractions, and students often make the "mistake" of doing this when in some cases, such as this one, it is unnecessary. The solution discusses this issue.