4. Evaluate the following integrals: (a) s 213cosy da siny (b) ſ sec8(tand + sec8 +...
4. Evaluate the integrals that converge. +00 -4. e da (b) (b) Si Jo-1 da (18 pts.)
Q2- Evaluate the integrals: (a) ſ sinᵒ x.cos x. dx (b) ſ sin 8x. sin 5x.dx
ex4.19
Ex. 4.19. Use contour integration to evaluate the following real integrals dar da (a) (b) r22x5 (x21)2 da da (c) (d) (221)(a2+4)
Ex. 4.19. Use contour integration to evaluate the following real integrals dar da (a) (b) r22x5 (x21)2 da da (c) (d) (221)(a2+4)
8. Evaluate the given integrals. Show all work: 8. Evaluate the given integrals. Show all work: (a) ſ 1 der x Inc (e) der 2+1 [" sin cos x de
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)
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
5. Evaluate (a) [e-ar'de (b) ſ 2 sec(3x)da (c) de given y = e(x+5)(x2-3)
Evaluate the line integral ſ vydr for the following function s and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) с using the Fundamental Theorem for line integrals XY.2) - * 7x for sts 4 4 2 C: (0 cost, sint, Uning either methods, ſv • dr - C (Type an exact answer
Evaluate the following integrals. If the integral is divergent, state so. Make sure to clearly show all steps for full credit. (a) | 22 In zde (b) ſ sinº cosº o de (e) [ 74 - gyva dy (4 - y2)3/2 t •dt
Problem 2. Evaluate the following integrals: a) (t+1)8(t-1)dt b) ſ exp(-+)$(t + 2)dt c) Itsin() 062 – 1)dt