I need help with complex analysis integral and semicircle. Thankyou for explaining clearly. 3. Evaluate the integral001dx(x + i)²001by considering o DE) dz , where C(R) is the closed semicircle in the upper half plane with\(z+i)².C(R)corners at z = -R and z = R , plus the x axis. Hint: Show that:Sam1dz = 0lim(z + i)²C1(R)where C1(R) is the open semicircle in the upper half plane. (not including x axis).

Answered: 3. Evaluate the integral 1 (x + i)2 -00

Math

Advanced Math

3. Evaluate the integral 1 (x + i)2 -00

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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I need help with complex analysis integral and semicircle. Thankyou for explaining clearly.

3. Evaluate the integral
00
1
dx
(x + i)²
00
1
by considering o DE) dz , where C(R) is the closed semicircle in the upper half plane with
\(z+i)².
C(R)
corners at z = -R and z = R , plus the x axis. Hint: Show that:
Sam
1
dz = 0
lim
(z + i)²
C1(R)
where C1(R) is the open semicircle in the upper half plane. (not including x axis).

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

Given:

$\int_{- \infty}^{\infty} \frac{1}{{(x + i)}^{2}} d x$

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