Pre-Calc Homework Solutions 220

Pre-Calc Homework Solutions 220 - 220 Section 5.4 17. Graph...

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Unformatted text preview: 220 Section 5.4 17. Graph y x3 3x 2 2x. 1 13. 1 (r 4 1)2 dr u u 1 (r 3 4 1)3 1/2 1 1 8 3 0 8 3 14. 0 1 du 0 (u 2u1/2 (4 1) du 4 u 0 [0, 2] by [ 1, 1] 4) (0 0) 0 Over [0, 1]: 1 0 15. Graph y 2 x. (x 3 3x 2 2x) dx 1 4 x 4 x3 x2 1 0 1 4 0 1 4 Over [1, 2]: 2 1 (x 3 3x 2 1 4 2x) dx 1 4 [0, 3] by [ 2, 3] 2 Total area 1 2 x 2 1 2 x 2 2 1 4 x 4 1 2 x3 x2 2 0 1 1 4 1 4 18. Graph y 2 x3 4x. Over [0, 2]: 0 (2 3 x) dx x) dx 1 2 5 2 2x 2x 0 3 2 Over [2, 3]: 2 (2 2 3 2 2 1 2 [ 2, 2] by [ 4, 4] Total area 16. Graph y 3x 2 3. Over [ 2, 0]: 0 2 (x 3 4x) dx 1 4 x 4 2x 2 0 0 2 ( 4) 4 Over [0, 2]: 2 [ 2, 2] by [ 4, 10] 0 (x 3 4x) dx 4 x2 x 1 4 x 4 2x2 8 2 4 0 0 4 Over [ 2, 1 2 1]: 3) dx x3 1 Total area 3x 2 4 (3x 2 2 ( 2) 4 19. (a) No, f (x) (b) x2 x 1 1 1 is discontinuous at x 1 1. Over [ 1, 1]: 1 1 2 x 1, x 1 (3x 2 3) dx (3x 2 x3 3x 1 1 2 x3 2 2 4 The area between the graph of f and the x-axis over [ 2, 1) where f is negative is (3)(3) 1 2 9 . The area 2 Over [1, 2]: 1 3) dx 3x 1 2 ( 2) 4 between the graph of f and the x-axis over (1, 3] where f is positive is (2)(2) 1 2 2. 2 5 2 Total area 4 4 4 12 3 2 x x 2 1 dx 1 9 2 20. (a) No, f (x) (b) 9 x2 3x 9 9 x2 is discontinuous at x 3x 9 3 3 x 3. ,x 3 1 and Note that f is negative for x in [0, 5]. f (0) f (5) 8 . The area between the graph of f and the 3 1 8 55 x-axis over [0, 5] is (5 0) 1 2 3 6 5 55 9 x2 dx 6 9 0 3x ...
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