# Contours and the Cauchy Integral Formula

Let C be the boundary of the square of side length 4, centered at the origin, with sides parallel to the coordinate axes, and traversed counterclockwise. Evaluate each of the attached integrals.

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Contours and the Cauchy Integral Formula are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Complex Integrals - Cauchy's Integration Formula

Three questions to do with Cauchy's integral formula are evaluated in clear, easy to understand steps.

1. Show that

see attached

where C is the semicircule |x|=R>1, lm(x)>=0 from x=-R to z=R.

2. Use Cauchy's integral formula for derivatives to evaluate

see attached

where |z-2|=2 is oriented clockwise.

3. Evaluate

see attached

where C is the square with vertices 2+/-2i, -2+/-2i, oriented counterclockwise