# Complex Integrals - Cauchy's Integration Formula

Not what you're looking for? Search our solutions OR ask your own Custom question.

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

https://brainmass.com/math/complex-analysis/complex-integrals-cauchys-integration-formula-574015

#### Solution Summary

This solution reviews some basic properties of line integration, including the Cauchy integration formula for derivatives. Then a detailed solution is presented for each of the three questions to show by example how to apply these properties.

$2.49