Jo at 12. Residue theorem. Compute the following integral, 80 (1 +4232(2 points)
please 2 only, thanks
Exercises dA (1) Use Cauchy's residue theorem to compute Jo 2+sin (2) Repeat the preceding exercise for 8" 131. (3) Let a be a complex number such that lal < 1. Prove that (2 27 Jo 1 - 2a cos 0 + a2d6 = 1 - 22 (4) What is the value of the integral in the preceding exercise when |al > 1? (Hint: Let b= 1.)
Show that
using Cauchy Residue Theorem.
(p-over-q rule or phi-rule)
Jo x4 +1 22
Jo x4 +1 22
Compute the following using the residue theorem (complex
analysis):
2. More integrals! Evaluate each integral, using either a Cauchy Integral Formula or Cauchy's Residue Theorem. Take C to be the circle [2] = 3, oriented counter-clockwise. 1) Sota-1jad: 6) Se TH h) Sorºcos(1/2)da
Use the residue theorem to compute the next definite
integral
please don't skip any steps and answer thoroughly
cos(a.x) som (a > 0, b>0). (22 +62)2d.t
solve a and c only
1. Use the residue theorem to evaluate the following integrals: cos θ (2+sin θ) 2n 0 0 1+sin2 θ 2x-0820, de (C) Jo 5-4cos
19 = 1 7. (15 points) Sections 6.4-6.6 Use the residue theorem to calculate the following integrals. a. 1 = 1 d 2 +9 dar b. 12 = 1. <+1) h c. Cos 2x da 2? + 4 2i Vr+e? da x2 + 4 d. 1 = 2 va + che de
Evaluate the integral using residue theorem , be sure to specify
poles and orders
| 16dx Jooo (x2+4)3
roo cos(x) CO Use the Residue Theorem to compute dx -00 X21 CO
roo cos(x) CO Use the Residue Theorem to compute dx -00 X21 CO
Problem 3. Evaluate the integral co sinx dx. Hint: Apply residue theorem to the function f(z) = and the contour y of the following shape: