Pre-Calc Homework Solutions 432

Pre-Calc Homework Solutions 432 - 432 27. Section 10.6 30....

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Unformatted text preview: 432 27. Section 10.6 30. The integral given is incorrect because r out the circle twice as cos sweeps goes from 0 to 2 . Or, you can't use equation (2) from the text on the interval [0, 2 ] [ 9, 9] by [ 6, 6] because r cos is negative for To find the integration limits, solve 3 csc , 6 3 5 . The correct area is , which can be found 2 2 4 3 by computing the areas of the cardioid and the circle 2 4 5 . The area in question is 6 6 5 /6 1 2 (6 32 csc2 ) d /6 2 5 /6 1 36 9 cot 2 /6 separately and subtracting. dr d 31. 2 , so 5 Length 0 5 ( 2)2 2 (2 )2 d 4d 5 0 12 28. 9 3 0 1 2 ( 3 1 (27 3 [ 3, 3] by [-2, 2] 4)3/2 8) 19 3 To find the intersection points, solve 6 cos 2 48 cos4 cos 2 32. dr d e 2 , so e 0 9 sec2 4 2 Length 9 0 0 e 2 2 d 2 24 cos2 3 4 e d e 0 e 1 6 /6 . 33. dr d By the symmetry of the curves, the area in question is 2 0 sin , so 2 1 6 cos 2 2 3 sin 2 9 tan 4 9 sec2 4 /6 0 d 3 4 3 Length . 0 2 (1 2 0 2 cos )2 2 cos 4 cos2 2 2 ( sin )2 d d , 29. (a) Find the area of the right half in two parts, then double the result: Right half area /4 0 2 0 2 2 2d 1 tan2 2 /2 d /4 1 1 csc2 2 2 /2 d 2 cos 0 d d 8 1 tan 2 1 1 2 4 /4 0 1 4 cot /4 4 0 cos 2 1 (0 4 1) 3 2 3 4 4 8 . 34. dr d 8 sin 0 Total area is twice that, or (b) Yes. x y . a sin 2 0 cos 2 , so 2 tan sin x 1, cos y 1, x sin2 cos sin Length a 0 a2 sin4 sin2 cos 2 2 a2 sin2 d 2a 0 2 cos2 2 d tan lim /2 lim /2 y 2a /2 lim x /2 lim y ...
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