Pre-Calc Homework Solutions 222

Pre-Calc Homework Solutions 222 - 222 x Section 5.4 x 35. a...

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Unformatted text preview: 222 x Section 5.4 x 35. a f (t) dt x K b f (t) dt x 43. Choose (d). dy dx d dx x e e t2 t2 dt 3 3 0 e x2 K a a f (t) dt b x f (t) dt f (t) dt b y( ) dt 3 3 f (t) dt x a f (t) dt b 1 44. Choose (c). dy dx d dx x sec t dt 1 1 4 4 sec x 0 4 4 K 2 (t 2 3t 3 2 t 2 3 2 1) dt 1 y( 1) 1 sec t dt 1 3 t 3 1 3 t 2 ( 1) 8 3 6 2 3 2 45. Choose (b). dy dx d dx x sec t dt 0 0 4 4 0 sec x 4 4 36. To find an antiderivative of sin2 x, recall from trigonometry that cos 2x 0 y(0) 0 sec t dt 1 2 sin2 x, so sin2 x 1 2 1 cos 2x. 2 46. Choose (a). dy dx d dx x K 2 sin t dt 0 2 2 e 1 1 t2 t2 dt 3 3 0 0 e x2 y(1) 1 2 1 cos (2x) dx 2 1 sin (2x) 4 0 2 0 2 1 e a since dt 3 3 a 47. x 48. f (x) f (t) dt a x 1 x 2 1 x 2 1 sin x cos x 2 d dx f (t) dt 1 x 0 d 2 (x dx 10 2x 10 1 x 1) 2x 2 49. f (x) sin 2 cos 2 2 2 0 dy 37. dx dy 38. dx d dx 1 1 1 x sin 2 cos 2 2 d 2 dx 1 t dt 1.189 f (0) f (0) L(x) 10 0 x 2 2 0 10 1 t dt 2 2 10x x 1 dt t d dx d ( dx x 1 1 dt t 1 x 1 1/2 x 2 sin x 2 x 50. f (x) 39. 40. dy dx dy dx sin ( x)2 cos (2x) d dx x 0 3 x) (sin x) d f (t) dt dx 0 d (x cos x) dx d (2x) dx 2 cos (2x) x 2 x( sin x) x sin x 1 cos x cos x cos 4 1 0 to x /k 0 dy 41. dx cos (2t) dt 0 cos (2t) dt cos (2x ) 2x 2 f (4) 4 sin 4 cos (2x ) 3x 3x cos (2x ) dy dx d dx d dx cos x sin x cos x 0 3 2 2 3 2x cos (2x 2) 51. One arch of sin kx is from x /k k . 1 k 1 k 2 3 Area 0 sin kx dx 2 1 cos kx k 2 k 42. t 2 dt t 2 dt sin x 0 t 2 dt 52. (a) 3 (6 x x 2) dx 6x 22 3 125 6 cos2 x ( sin x) sin x cos2 x sin2 x cos x 1 2 x 2 27 2 1 3 x 3 sin2 x cos x ...
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