Question

Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of the following integrals. It is necessary to consider several cases. THOUGH APPLICABLE, DO NOT APPLY THE RESIDUE THEOREM IN THIS EXERCISE. i) \( \int_C \frac{dz}{z^2 + 4} \) ii) \( \int_C \frac{dz}{z(z^2 - 1)} \) iii) \( \int_C \frac{e^z}{z^2 + 9} dz \)

          Problem 23.
Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of the
following integrals. It is necessary to consider several cases. THOUGH APPLICABLE, DO
NOT APPLY THE RESIDUE THEOREM IN THIS EXERCISE.
i) \( \int_C \frac{dz}{z^2 + 4} \)
ii) \( \int_C \frac{dz}{z(z^2 - 1)} \)
iii) \( \int_C \frac{e^z}{z^2 + 9} dz \)

Problem 23.
Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of the
following integrals. It is necessary to consider several cases. THOUGH APPLICABLE, DO
NOT APPLY THE RESIDUE THEOREM IN THIS EXERCISE.
i) (dz)/(z^2 + 4)
ii) (dz)/(z(z^2 - 1))
iii) (e^z)/(z^2 + 9) dz

Added by Donald M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

Step 1

First, we need to determine the poles of the integrand. The denominator C^2 + 4 can be factored as (C + 2i)(C - 2i). Therefore, the poles are at C = -2i and C = 2i. Show more…

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Problem 23. Answer using Cauchy's Theorem. Given that C is a simple closed path, evaluate each of the following integrals. It is necessary to consider several cases. THOUGH APPLICABLE, DO NOT APPLY THE RESIDUE THEOREM IN THIS EXERCISE. i) âˆ« dz / (C^2 + 4) ii) [No text provided]