Pre-Calc Homework Solutions 430

Pre-Calc Homework Solutions 430 - 430 Section 10.6 2 (as...

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Unformatted text preview: 430 Section 10.6 2 (as can be verified 19. 13. The curve is complete for 0 by graphing). The area is 2 0 1 (4 2 2 2 cos )2 d (4 4 cos 4 sin 1 2 2 0 cos2 ) d 1 sin 2 4 2 [ 2.5, 5.2] by [ 2, 3.1] 2 4 18 0 The circles intersect at (x, y) coordinates (0, 0) and (1, 1). The area shared is twice the area inside the circle r 2 sin 2 0 /4 14. The curve is complete for 0 by graphing). The area is 2 0 2 (as can be verified between /4 0 and 4 . 1 2 a (1 cos )2 d 2 2 1 2 a (1 2 cos 2 0 1 2 1 a 2 sin 2 2 Shared area cos2 ) d 1 sin 2 4 2 0 1 (2 sin )2 d 2 4 sin2 d /4 0 0 3 2 a 2 4 4 20. 1 2 1 sin 2 4 1 4 15. Use r 4 2a2 cos 2 . One lobe is complete for 4 8 2 1. . The total area is 2 2 /4 2 1 ( /4 2 2a cos 2 ) d 2a 2 /4 cos 2 d /4 2a2 1 sin 2 2 /4 /4 2a2 (Integrating from 0 to 2 will not work, because r is not defined over the entire interval.) 16. One leaf covers /4 [ 3, 3] by [ 2, 2] The circles intersect at 1, 4 1 4 1 cos2 2 d /4 2 4 1 sin 4 16 6 and 1, /2 /6 5 . The shared area 6 . Its area is /4 /4 /6 is 2 8 . 4 2 0 1 (2 sin )2 d 2 2 /2 /6 1 2 (1) d 2 /6 0 sin2 d /6 0 d /2 /6 17. Use r Its area is 4 sin 2 . One loop is complete for 0 /2 0 . 1 ( 2 4 sin 2 )2 d 0 /2 4 2 3 1 2 2 sin 2 d /2 cos 2 0 2. 21. 3 1 sin 2 4 3 2 3 3 2 3 18. Use r 2 sin 3 . One leaf is complete for 0 . The total area is /3 6 0 1 ( 2 2 sin 3 )2 d /3 6 0 sin 3 d /3 [ 4.7, 4.7] by [ 3.1, 3.1] 2 cos 3 0 4. The shared area is half the circle plus two lobelike regions: 1 (2)2 2 /2 2 0 /2 1 [2(1 2 cos )]2 d 4 cos2 ) d 1 2 1 sin 2 4 /2 0 2 0 (4 4 8 8 cos 2 sin 2 5 ...
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