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evaluate-C-z-2-sin-z-cos-z-z-2-1-z-2-1-dz-where-C-z-C-z-2-

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Question Number 191 by 123456 last updated on 25/Jan/15
evaluate ∫_C ((z^2 sin z cos z)/((z^2 +1)(z^2 −1)))dz where C={z∈C∣∣z∣=2}
evaluate∫Cz2sinzcosz(z2+1)(z2−1)dzwhereC={z∈C∣∣z∣=2}
Answered by nileshkulkarni last updated on 15/Dec/14
Apply Residue theorm. Poles of the fuction are z= i. z=−i. z=1. z=−1 evaluating the fuction at these four poles and then adding it gives 0
ApplyResiduetheorm.Polesofthefuctionarez=i.z=−i.z=1.z=−1evaluatingthefuctionatthesefourpolesandthenaddingitgives0

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