Directions: Answer these questions without using your calculator. 1. ( 3 x - 2x + 3 ) dx = (A) x-x2 + C (B) 3x - x2 + 3x + C (C) x3-x2+ 3x + C (D) - (3x2 - 2x + 3)2 + C (E) none of these 2. x - 1 dx = (A) x - - 1 3 + C (B) 2-1+ + C (C) - -2x - 1 - + C 2x 4x (D 3 -x - -+C (E) none of these 3. V4 - 2t di = (A) -= (4-21) 32 + C (B) 3 - (4 - 21) 32 + C (C) -- (4-2t)3 + C (D) 2 +1 (4-21) + C (E) 4 (4-21) 312 + C 4. (2 - 3 x)' dx = (A) - (2-3x) + C (B) - (2 - 3x) + C (C) = (2 - 3x ) 6 + C (D) 1 18 (2-3x) + C (E) none of these 1 - 3y 5. V2y - 312 dy = (A) 412y - 3y2 + C (B) - (2y - 3,3 )2 + C (C) - In2y - 3y2 + C (D) - (2y - 3)2) 12 + C (E) 2y - 3y2 + C\f23. sin 0 cos 0 de = (A) 8 - UIS -+ C (B) - cos 20 + C (C) cos- 0 -+ C 2 2 (D) - sin 20 + C (E) cos 20 + C 24. sin VX dx = Vx (A) -2 cos" x + C (B) - cos Vx + C (C) -2 cos Vx + C (D) 2 sin " x + C (E) -cos VX + C 2 25. t cos ( 21)3 dt = 8 (A) - sin (4/) + C (B) cos' (21) + C (C) -- sin (4/) + C 8 (D) - sin (2t)3 + C (E) none of these . cos' 2x dx = (A) ~ + Sin 4x -+ C sin 4x (B . + C (C) -+ . sin 4x 2 8 4 -+ C + 1 (D) x sin 4.x A -+ C (E) 16 (x + sin4x) + C 27. sin 20 de = (A) cos 20 + C (B) -2 cos 20 + C (C) -sin3 0 + C (D) cos' 0 + C (E) 2 --cos 20 + C 28. x cos x dx = BC ONLY (A) x sin x + C (B) x sin x+ cos x+ C (C) x sin x-cosx+ C D) cos x - x sin x + C (E) 2 - sin x + C 29 Cos- 3u (A) sec 3u + C (B) tan 3u + C (C) u+ sec 3u - + C 3 3 (D) tan 3u + C (E) + C 3 cos 3u36. dx sin- 2x . (A) - csc 2x cot 2x + C (B) 2 +C (C) 2 cot 2x + C sin 2x 2 (D) -cot x + C (E) -csc 2x + C 37. tan" & dy = It p ? (A) sec-ly + C (B) (tan- y)' + C (C) In (1 + y) + C D) In (tan-ly) + C (E) none of these 38. sin 20 cos 0 de = (A) cos' 0 + C (B) 2 cos' 0 + C (C) sin @ cos 0 + C (D) cos' 0 + C (E) none of these 39. sin 21 di = 1 - cos 2t . 2 (A) + C (1- cos 21)2 - In 1 - cos 2t| + C (C) In [1 - cos 2/| + C (D) VI - cos 2t + C (E) 2In1 - cos 21| + C 40. cot 2u du = (A) Insinu) + C (B) - In/sin 2ul + C (C) --csc? 2u + C (D) -sec 2u + C (E) 2 In sin 2u| + C. 41. edx= (A) x+ Ine' -1+C (B) x-e'+C (C) x - (ex - 1)37 i+c (D) 1+- 1 - + C (E) In|ex - 1+ C 42. x - 1 dx = BC ONLY x(x - 2) (A) - In/x/ + In/x - 2| + C (B) IIn * - 2 + C 2 x (C) In/x - 2/ + In/x| + C (D) !In(x(x - 2)|+ c (E) none of these\fcos 8 68. 1 + sine 0 = (A) sec 0 tan 0 + C (B) sin 0- csc 0 + C (C) In (1 + sin' 0) + C (D) tan-' (sin 0) + C (E) + C (1 + sin' 0) 69. arc tan x dx = (A) arc tan x + C (B) x arc tan x - In (1 + x]) + C (C) x arc tan x + In (1 + x) + C (D) x arc tan x + - In (1 +x) + c 2. (E) x arc tan x - -In (1 +x) + C 2 70. dx (A) - In1- e"+ c (B) x - In1- e|+ c (C) 1 + C (1 -e* )2 (D) e" Inte | +C (E) none of these 71. (2 - >) dy = ( A ) ( - VVY+ C (B) 2, y - 2312 + 8512 + C (C) Inly|- y + 2yz + C (D) 21 12 _ 2 32 1 512 + C $ 10 (E) none of these 72. ethan du = (A) + C (B) . (c) - u' 3 2 (D) 21m# + C el+2lma + C. 73. dy y(1 + In y?) (A) - In 1 + Iny?| + C (B) 1 + C (1 + In y? )2 (C) Inly/+ - InIny|+ C (D) tan-'(Inly)+ C (E) none of these74. (tan 0 - 1)' de = (A) sec 0 + 0+ 21ncos0| + C (B) tan0 + 2In|cose|+ C (C) tan 0 - 2 sec' 0 + C (D) sec 0 + 0 - tan' 0 + C (E) tan 0 - 2 In cos e| + C 75. de I + sin 0 = (A) sec 0 - tan 0 + C (B) In (1 + sin 0) + C C) In sec 0 + tan 0 + C (D) 0+ In/csc0 - cote| + C E) none of these 76. A particle starting at rest at / = 0 moves along a line so that its acceleration at time t is 12/ ft/sec. How much distance does the particle cover during the first 3 sec? (A) 16 ft (B) 32 ft (C) 48 ft (D) 54 ft (E) 108 ft 77. The equation of the curve whose slope at point (x, y) is a - 2 and which contains the point (1, -3) is (A) 13 - 2x (B) y= 2x- 1 (C) y= 10 3 (D) y = - - 2x (E) 3y=x - 10 78. A particle moves along a line with acceleration 2 + 6/ at time . When / = 0, its velocity equals 3 and it is at position s = 2. When f = 1, it is at position s = (A) 2 (B) 5 (C) 6 (D) 7 (E) 8 79. Find the acceleration (in ft/sec') needed to bring a particle moving with a velocity of 75 ft/sec to a stop in 5 sec. (A) -3 (B) -6 (C) -15 (D) -25 (E) -30 80. 72 - dx= BC ONLY (A) x+-In Ix + 1/ *+ (B) Inx-1+c (C) x+ tan- x + C ) xt- In *+1 ( E ) It #+ 1) H+ c 2 Lx - 1 x - 1