







solve a and c only 1. Use the residue theorem to evaluate the following integrals: cos...
use residue theorem to evaluate the following
integrals
16) cosa 30 de 5- 4 cos 20 17) COSI det (x + 1)? sin 3x dx 18) sin x dx (x² + 4x+5 19)
4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c)
4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c)
use residue theorem to evaluate the following
integrals
sin z 21) 20) Cosx dx (r? + 1) X 22) sin mx dx 2(x² + a²² (a > 0, b>0) 23) cos ex - cos bx -dx x?
5. Use Cauchy's residue theorem to evaluate the following integrals along the circle 121 = 4: C 22
5. Use Cauchy's residue theorem to evaluate the following integrals along the circle 121 = 4: C 22
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
2.6 Exercise. [Paul Use Theorem 9.35 and then Remark 9.34 to evaluate the following integrals (for some a, b e R such that a < b) 1. ( cos (r - log (x)dr 3. s 2 (3 - 10 dr 5. S sin (1-) (2-cs( ))dr 6. cos (3r) (si(3) 3-tan(4) a cos(4) 7 a (5r2+4) 14 15
2.6 Exercise. [Paul Use Theorem 9.35 and then Remark 9.34 to evaluate the following integrals (for some a, b e R such...
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.)
9. (12 pts) Evaluate the following definite and indefinite integrals: (a) 12 dt d dx 1* 2 t Hint: Apply Part 1 of the Fundamental Theorem of Calculus and the Chain Rule. (b) /6 sin 20 de (sin2 @ + 2)2 -
Thanks
6. Use residue theory to compute each of the following real integrals: cos() dr
6. Use residue theory to compute each of the following real integrals: cos() dr
DO
NOT use a calculator. Exact answers only, no decimals.
1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr
1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr