Pre-Calc Homework Solutions 295

Pre-Calc Homework Solutions 295 - Section 7.2 10. Integrate...

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Unformatted text preview: Section 7.2 10. Integrate in three parts: 1 295 13. Solve 7 x 1. 1 2x 2 x2 4: x 2 1, so the curves intersect at [( x 2 2 2) (4 x )] dx 2 [(7 1 2x 2) (x 2 1 4)] dx 1 ( 3x 2 1 3) dx x 2) dx [(4 1 3 x 2) ( x 2)] dx 3 (1 1 [( x 2 1 2) (4 x 2)] dx 2 3 x 2 1 3 x 3 1 1 (x 2 3 2 2 x 2) dx 1 ( x x 2) dx 14. 3 2 3 2 3 4 (x 2 x 1 2 x 2 1 x2 2 1 2 2) dx 1 1 3 x 3 1 x3 3 1 3 8 3 2x 2 3 1 3 x 3 1 x2 2 2 2x 1 [ 3, 3] by [ 1, 5] 2x 2 The curves intersect at x 8 3 1 3 1 and x 2. Use the 2 2 1 2 4 region's symmetry: 2 [(x 4 0 1 4x 2 5x 2 5 3 x 3 5 3 4) x 2] dx 2 2 [x 2 1 2 (x 4 5x 2 4x 2 4) dx 2 4)] dx 2 9 2 4 8 3 2 2 (x 4 0 1 4) dx 1 2 ( x4 1 9 49 6 6 2 4 2 x5 1 2 5 1 5 4x 0 2 32 5 1 5 x 5 40 3 5 3 x 3 4x 1 8 1 6 4 2 8 1 5 5 3 4 8 15. 2 2: x 2 4, so the curves intersect at 11. Solve x 2 x 2 2. [2 2 (x 2 2 2)] dx 2 (4 8 8 3 x 2) dx 8 8 3 32 3 4x 1 3 2 x 3 2 10 2 3 3 3 a, a by [ a 2, a 2] 2 2 The curves intersect at x 0, symmetry: 2 x a2 0 a 0 and x a. Use the region's 12. Solve 2x x2 3: x 2 2x 3 (x 3)(x 3. 3 1 1) so the curves intersect at x 3 1 and x 1 3 x 3 x 2 dx 2 2 0 1 2 (a 3 x 2)3/2 1 3 a 3 a 0 (2x 1 x 2 3) dx x (9 2 3x 1 9 10 2 3 9) 1 3 3 2 3 a 3 32 3 ...
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