Question

Let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2. Evaluate each of these integrals: (a) ∫ e^-z dz / (z - (πi/2)) (b) ∫ cos(z) dz / [z(z^2 + 8)] (c) ∫ z dz / (2z + 1) (d) ∫ cosh(z) dz / z^4 (e) ∫ tan(z/2) dz / (z - x_0)^2 (-2 < x_0 < 2) Ans. (a) 2π; (b) πi/4; (c) -πi/2; (d) 0; (e) iπ sec^2(x_0/2)

Name: let c denote the positively oriented boundary of the square whose sides lie along the lines x 2 and y 2 evaluate each of these integrals e d cos z 2 dz a b jczaz8 dz c jezzr cz 7i2 coshz d 53968
Uploaded: 2022-01-21T10:41:03-08:00
Duration: 6 min 11 s
Channel: Krishna S
Description: let c denote the positively oriented boundary of the square whose sides lie along the lines x 2 and y 2 evaluate each of these integrals e d cos z 2 dz a b jczaz8 dz c jezzr cz 7i2 coshz d 53968

          Let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2. Evaluate each of these integrals:
(a) ∫ e^-z dz / (z - (πi/2))
(b) ∫ cos(z) dz / [z(z^2 + 8)]
(c) ∫ z dz / (2z + 1)
(d) ∫ cosh(z) dz / z^4
(e) ∫ tan(z/2) dz / (z - x_0)^2 (-2 < x_0 < 2)

Ans. (a) 2π; (b) πi/4; (c) -πi/2; (d) 0; (e) iπ sec^2(x_0/2)

Added by Stacey D.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Krishna S

01/21/2022

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Let C denote the positively oriented boundary of the square whose sides lie along the lines x = ±2 and y = ±2. Evaluate each of these integrals: (a) ∫ e^-z dz / (z - (πi/2)) (b) ∫ cos(z) dz / [z(z^2 + 8)] (c) ∫ z dz / (2z + 1) (d) ∫ cosh(z) dz / z^4 (e) ∫ tan(z/2) dz / (z - x_0)^2 (-2 < x_0 < 2) Ans. (a) 2π; (b) πi/4; (c) -πi/2; (d) 0; (e) iπ sec^2(x_0/2)