Pre-Calc Homework Solutions 437

Pre-Calc Homework Solutions 437 - Chapter 10 Review 29. r 4...

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Unformatted text preview: Chapter 10 Review 29. r 4 tan sec r sin 4 r cos dr d 437 37. sin , so 2 r cos x y 4 or x 2 x Length 0 2 ( 1 2 cos )2 2 cos 2 ( sin )2 d 4y, a parabola d 2 30. r cos r cos cos 3 3 3 2 2 3 r sin sin 2 3 0 2 0 4 sin2 d 4 cos 2 8. 0 2 3 38. 1 r cos 2 1 3 x y 2 2 r sin 3 3 dr d 0 0 2 cos /2 2 sin , so Length 2 cos )2 8 cos2 2. d (2 cos 2 sin )2 d (2 sin /2 /2 2 4 8 sin2 2 2d x 31. x r2 r 2 3y 2 3 or y 0 0 0 0 x 3 4, a line 0 y 5y 5r sin 5 sin 39. dr d 8 sin2 3 /4 cos 3 , so 2 32. x 2 y 2 2y r 2 2r sin r 2 sin 33. x 2 Length 0 /4 0 8 sin3 8 sin2 8 sin2 3 3 3 8 sin2 3 2 3 cos 3 3 d sin2 d cos2 d 4y 2 2 16 4(r sin ) 4r 2 sin2 (y 2)2 2 /4 (r cos ) r 2 cos2 34. (x 2)2 (r cos 35. 16 16, or r 2 cos2 16 4 sin2 0 8 1 2 3 2 sin 4 3 /4 3 0 5)2 16 (r sin 5)2 e t, so 2e2t 1 2t e 2 1 2 8 1 2 8 1 64 16 40. dr d /2 sin 2 1 /2 , so Length cos 2 )2 1 sin 2 cos 2 2 c os 2 dx = 2e2t dt 1 dy , 8 dt ln 2 0 ( 1 (et )2 dt e dt 2t /2 /2 /2 /2 d Length ln 2 0 ln 2 0 (1 1 1 cos 2 )2 cos 2 2 cos 2 1 sin2 2 d 1 cos 2 cos2 2 cos 2 sin2 2 4e 4t d 2e2t t 8 ln 2 8 ln 2 8 ln 2 0 dt /2 2d /2 2 dy dt e 4 3 2t 41. 1 ln 2 8 24 dx dt 2 sin t, /2 0 /2 2t, so (2t)2 dt Length 3.087. 0 ( 2 sin t)2 2 t2 sin2 t dt, 3.183. which using NINT evaluates to dx 36. dt dy 2t, dt 3 t 2 1, so 42. (2t) 2 Length 3 3 (t t4 2 2 1) dt 2t 2 1 dt 2 dx dt 3 cos t, 3 0 dy dt 3 t, so (3 t)2 dt 12.363. 3 Length (3 cos t)2 3 0 t cos2 t dt, 4t 2 3 3 which using NINT evaluates to 2 (t 3 2 3 1) dt 4 3 43. Area 0 t 3 3 t 3. 1 (4 4 cos 2 0 1 4 4 sin 2 1 (2 2 2 cos )2 d cos2 ) d 1 2 1 sin 2 4 2 0 9 2 ...
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