use the contour integration and theory of residues to evaluate
Since the answer is too lengthy there will be some chance of
some errors(I have avoided every errors as much i can)So please go
through the answers and understand each step
use the contour integration and theory of residues to evaluate too COS Xdx -O [1+ x41
Use contour integration to evaluate the integral 2T 1 I (5 4 cos (0))2 S 0 diagram showing the contour and the singularities Draw and label a For your information, the graph of the integrand is given below. L0- 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1. 7T 2n 4. -
Use contour integration to evaluate the integral 2T 1 I (5 4 cos (0))2 S 0 diagram showing the contour and the singularities Draw and label a For...
COS Use a contour to evaluate dr (2° +1)
2x 1 Use a contour to evaluate dᎾ (2+0 -cos)
.21 1 Use a contour to evaluate S2 d8 (?+cos 8)2
Problem 1 Use residues to verify the formula poo cos(3x) – cos(x) dx = a Jo x² Hint: use the indented contour with two semicircles from the April 14 lecture. Problem 2 Use residues to verify the formula [ * nedz =
Complex Analysis
Use a contour to evaluate $25 1 (2+cos 0) dᎾ
Show that the following integral has the solution, using contour integration in the complex plane: 2.π dx 9-V 3 Determine a fitting path of integration Hint: Show that the sum of the residue/residues of the singular point/points of the 2.T-1 integrand is and use (if appropriate) finally that sin3 -2 to calculate the integral.
Show that the following integral has the solution, using contour integration in the complex plane: 2.π dx 9-V 3 Determine a fitting path of integration Hint:...
1 Use a contour to evaluate So 27 0 dᎾ (2+cos 6)2
Yes find Integral in Complex analysis Or Complex Contour
Integration
5. Evaluate the integral of f along a contour y where f and y are given as follows. (a) f(x+iy) = eyel-ix along y, a positively oriented ellipse determined by the equation r = cos(20) +2. (b) f(z) = 223 (24 – 1)-2 along y(t) =t+iVt where 0 <t<1. [10] [6]
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d