Please #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29

\f21. tan x sec x dx 22 . tan'0 sec*0 de 61. If "/4 tan'x sec x dx = I, express the value of of* tan'x sec x dx in terms of 1. 23. tan x dx 24. (tan'x + tan'x) dx 62. (a) Prove the reduction formula 25. tan'x secox dx 26. "sec'0 tan'0 de [tan x dx = -tan -'x 2n - 1 tan en -2x dx 27. tan'x sec x dx tan'x sec'x dx (b) Use this formula to find tan'x dx. 63. Find the average value of the function f(x) = sin'x cos'x 29. tan'x sec'x dx 30. "tan t dt on the interval [- 7, 77]. 64. Evaluate / sin x cos x dx by four methods: 31. tan'x dx tan'x sec x dx (a) the substitution u = cos x (b) the substitution u = sin x - tanx (c) the identity sin 2x = 2 sin x cos x 33. 34. tan x sec x x (d) integration by parts sec-x cos x Explain the different appearances of the answers. 35. (#/4 sin'x .dx 36. sin 0 + tan 0 65-66 Find the area of the region bounded by the given curves. cos x cos'e 65. y = sin'x, y = sin'x, Ox S T "cot x dx 38. " cot'x dx 66. y = tan x, y = tan x, 0 x S T/4 39. #/2 cot'd csc'd db 40. csc*0 cotte de 67-68 Use a graph of the integrand to guess the value of the integral. Then use the methods of this section to prove that your 41. csc x dx 42. (W/3 C guess is correct. 67. " cos'x dx 68. sin 2 Wx Cos 5Tx dx 43. sin 8x cos 5x dx 44. sin 20 sin 60 de 45. cos 5t cos 10t dt 46. t cos'(t-) dt 69-72 Find the volume obtained by rotating the region bounded by the curves about the given axis. 47. ( sin (1/t) 2 . dt [sec? y cos'(tan y) dy 69. y = sin x, y = 0, T/2