Evaluate the given integral, where C is the circle with positive orientation. \displaystyle...
Question:
Evaluate the given integral, where {eq}C {/eq} is the circle with positive orientation.
{eq}\displaystyle \oint_C \frac{(5z - 3)^2}{(z^2 - 4)(z + 2)}\ dz,\ C: |z + 3| = 3 {/eq}
Complex Integral:
The Cauchy's Residue Theorem, which states that If, then we can use the given integral to find {eq}f(z){/eq} is analytic on and inside a simple closed curve {eq}C,{/eq} except a finite number of poles {eq}z_1,z_2,z_3\cdots z_n{/eq} within C then the integral {eq}\displaystyle \int _{C}f(z)\: dz=2\pi i\times \text{Sum of Residue} .{/eq}
Answer and Explanation: 1
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View this answerConsider the contour integral
{eq}\displaystyle \oint_C \frac{(5z - 3)^2}{(z^2 - 4)(z + 2)}\ dz,\ C: |z + 3| = 3 {/eq}
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{eq}\displaystyle...
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Definite Integrals: Definition
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Chapter 12 / Lesson 6
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A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.
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