4. Let C denote the positively oriented boundary of the square whose sides lie along the lines $x = pm 2$ and $y = pm 2$. Evaluate each of these integrals: (a) $int_C frac{e^{-z}}{z + (pi/2)} dz$ (b) $int_C frac{cos z}{z(z^2 + 16)} dz$ (c) $int_C frac{z}{2z - 5} dz$; (d) $int_C frac{cosh z}{z^5} dz$ $int_C frac{ an(z/2)}{(z - x_0)^3} dz$ ($x_0 in mathbb{R}, -2 < x_0 < 2)$.
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571), residue = e^{-z} evaluated at z=-Ļi/2 gives e^{Ļi/2}=i, so integral = 2Ļi * i = -2Ļ. Show moreā¦
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Evaluate the following integrals. State and verify the theorem(s) used, include a sketch of the given contour C where relevant. All curves are with anti-clockwise orientation unless stated otherwise.
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