Cauchy Integral Formula

(See attached file for full problem description and imbedded formulae) --- Why can (1) be regarded as a special case of (2)? (1) Cauchy's Integral formula (no need to prove): is a simple closed positively oriented contour. If is analytic in some simply connected domain D containing and if is any point inside , then (2) Cauchy's Residue Theorem (no need to prove): is a simple closed positively oriented contour and is analytic inside and on except at the points inside , then --- (See attached file for full problem description and imbedded formulae)

Residues for integral of exp & trig function

--- Using the method of residues, verify the following: --- (See attached file for full problem description)

Residues integral of trig function

Please see atached

Cauchy Integral Formula in an annulus

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Improper Integral

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