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.© BrainMass Inc. brainmass.com October 16, 2018, 7:46 pm ad1c9bdddf
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
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
where |z-2|=2 is oriented clockwise.
where C is the square with vertices 2+/-2i, -2+/-2i, oriented counterclockwise