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Pre-Calc Homework Solutions 318

# Pre-Calc Homework Solutions 318 - 318 8 Chapter 7 Review x...

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8. ˇ x w 1 ˇ y w 5 1 implies y 5 (1 2 ˇ x w ) 2 5 1 2 2 ˇ x w 1 x . [ 2 0.5, 2] by [ 2 0.5, 1] The area is E 1 0 (1 2 2 ˇ x w 1 x ) dx 5 3 x 2 } 4 3 } x 3/2 1 } 1 2 } x 2 4 5 } 1 6 } . 9. x 5 2 y 2 implies y 5 ! } 2 x } § . [ 2 1, 19] by [ 2 1, 4] The curves intersect at x 5 18. The area is E 18 0 1 3 2 ! } 2 x } § 2 dx 5 3 3 x 2 } 4 3 } 1 } 2 x } 2 3/2 4 5 18, or E 3 0 2 y 2 dy 5 3 } 2 3 } y 3 4 5 18. 10. 4 x 5 y 2 2 4 implies x 5 } 1 4 } y 2 2 1, and 4 x 5 y 1 16 implies x 5 } 1 4 } y 1 4. [ 2 6, 6] by [ 2 6, 6] The curves intersect at (3, 2 4) and (5.25, 5). The area is E 5 2 4 31 } 1 4 } y 1 4 2 2 1 } 1 4 } y 2 2 1 24 dy 5 E 5 2 4 1 2 } 1 4 } y 2 1 } 1 4 } y 1 5 2 dy 5 3 2 } 1 1 2 } y 3 1 } 1 8 } y 2 1 5 y 4 5 } 4 2 2 4 5 } 2 1 2 } 3 3 8 } 2 5 } 24 8 3 } 5 30.375. 11. [ 2 0.1, 1] by [ 2 0.1, 1] The area is E p /4 0 ( x 2 sin x ) dx 5 3 } 1 2 } x 2 1 cos x 4 5 } p 32 2 } 1 } ˇ 2 2 w } 2 1 < 0.0155. 12. 3 2 } p 2 } , } 3 2 p } 4 by [ 2 3, 3] The area is E p 0 (2 sin x 2 sin 2 x ) dx 5 3 2 2 cos x 1 } 1 2 } cos 2 x 4 5 4. 13. [ 2 5, 5] by [ 2 5, 5] The curves intersect at x < 6 2.1281. The area is E 2.1281 2 2.1281 (4 2 x 2 2 cos x ) dx , which using NINT evaluates to < 8.9023. 14. [ 2 4, 4] by [ 2 4, 4] The curves intersect at x < 6 0.8256. The area is E 0.8256 2 0.8256 (3 2 ) x ) 2 sec 2 x ) dx , which using NINT evaluates to
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