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Let A denote the negatively oriented triangle with vertices 0, 1, and i. Let Cr(20) denote the positively oriented circle centered at zo with radius r. (i.e. |zo|= r) Evaluate the following integrals. State clearly which theorem you are using. (a) Saidz (b) Sadz (c) SA 2-z-dz (d) Sc₁ (i) 42²+1dz dz (e) SC3/2(1+i) (z−1)(z−i)(z+i)( (f) and z+i sin z dz where is the path that consists of the two circles |2i| = 1 with positive orientation =1 with negative orientation. (g) dz where is the positively oriented rectangular path with vertices 4-i, 4+i, -4+i and -4-i. sin (h) (dz where is the positively oriented rectangular path with vertices -i, +i, −4+i and -4-i.

Let A denote the negatively oriented triangle with vertices 0, 1, and i. Let Cr(20) denote the positively oriented circle centered at zo with radius r. (i.e. |zo|= r) Evaluate the following integrals. State clearly which theorem you are using. (a) Saidz (b) Sadz (c) SA 2-z-dz (d) Sc₁ (i) 42²+1dz dz (e) SC3/2(1+i) (z−1)(z−i)(z+i)( (f) and z+i sin z dz where is the path that consists of the two circles |2i| = 1 with positive orientation =1 with negative orientation. (g) dz where is the positively oriented rectangular path with vertices 4-i, 4+i, -4+i and -4-i. sin (h) (dz where is the positively oriented rectangular path with vertices -i, +i, −4+i and -4-i.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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Let A denote the negatively oriented triangle with vertices 0, 1, and i. Let Cr(20) denote the positively oriented circle centered at zo with radius r. (i.e. |zo|= r) Evaluate the following integrals. State clearly which theorem you are using. (a) Saidz (b) Sadz (c) SA 2-z-dz (d) Sc₁ (i) 42²+1dz dz (e) SC3/2(1+i) (z−1)(z−i)(z+i)( (f) and z+i sin z dz where is the path that consists of the two circles |2i| = 1 with positive orientation =1 with negative orientation. (g) dz where is the positively oriented rectangular path with vertices 4-i, 4+i, -4+i and -4-i. sin (h) (dz where is the positively oriented rectangular path with vertices -i, +i, −4+i and -4-i.
Transcribed Image Text:Let A denote the negatively oriented triangle with vertices 0, 1, and i. Let Cr(20) denote the positively oriented circle centered at zo with radius r. (i.e. |zo|= r) Evaluate the following integrals. State clearly which theorem you are using. (a) Saidz (b) Sadz (c) SA 2-z-dz (d) Sc₁ (i) 42²+1dz dz (e) SC3/2(1+i) (z−1)(z−i)(z+i)( (f) and z+i sin z dz where is the path that consists of the two circles |2i| = 1 with positive orientation =1 with negative orientation. (g) dz where is the positively oriented rectangular path with vertices 4-i, 4+i, -4+i and -4-i. sin (h) (dz where is the positively oriented rectangular path with vertices -i, +i, −4+i and -4-i.
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