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Pre-Calc Homework Solutions 220

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

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13. E 1 2 1 ( r 1 1) 2 dr 5 3 } 1 3 } ( r 1 1) 3 4 5 } 8 3 } 2 0 5 } 8 3 } 14. E 4 0 } 1 2 ˇ ˇ u w u w } du 5 E 4 0 ( u 2 1/2 2 1) du 5 3 2 u 1/2 2 u 4 5 (4 2 4) 2 (0 2 0) 5 0 15. Graph y 5 2 2 x . [0, 3] by [ 2 2, 3] Over [0, 2]: E 2 0 (2 2 x ) dx 5 3 2 x 2 } 1 2 } x 2 4 5 2 Over [2, 3]: E 3 2 (2 2 x ) dx 5 3 2 x 2 } 1 2 } x 2 4 5 } 3 2 } 2 2 5 2 } 1 2 } Total area 5 ) 2 ) 1 ) 2 } 1 2 } ) 5 } 5 2 } 16. Graph y 5 3 x 2 2 3. [ 2 2, 2] by [ 2 4, 10] Over [ 2 2, 2 1]: E 2 1 2 2 (3 x 2 2 3) dx 5 3 x 3 2 3 x 4 5 2 2 ( 2 2) 5 4 Over [ 2 1, 1]: E 1 2 1 (3 x 2 2 3) dx 5 3 x 3 2 3 x 4 5 2 2 2 2 5 2 4 Over [1, 2]: E 2 1 (3 x 2 2 3) dx 5 3 x 3 2 3 x 4 5 2 2 ( 2 2) 5 4 Total area 5 ) 4 ) 1 ) 2 4 ) 1 ) 4 ) 5 12 17. Graph y 5 x 3 2 3 x 2 1 2 x . [0, 2] by [ 2 1, 1] Over [0, 1]: E 1 0 ( x 3 2 3 x 2 1 2 x ) dx 5 3 } 1 4 } x 4 2 x 3 1 x 2 4 5 } 1 4 } 2 0 5 } 1 4 } Over [1, 2]: E 2 1 ( x 3 2 3 x 2 1 2 x ) dx 5 3 } 1 4 } x 4 2 x 3 1 x 2 4 5 0 2 } 1 4 } 5 2 } 1 4 } Total area 5 ) } 1 4 } ) 1 ) 2 } 1 4 } ) 5 } 1 2 } 18. Graph y 5 x 3 2 4 x . [ 2 2, 2] by [ 2 4, 4] Over [ 2 2, 0]: E 0 2 2 ( x 3 2 4 x ) dx 5 3 } 1 4 } x 4 2 2 x 2 4 5 0 2 ( 2 4) 5 4 Over [0, 2]: E 2 0 ( x 3 2 4 x ) dx 5 3 } 1 4 } x 4 2 2 x 2 4 5 2 4 2 0 5 2 4 Total area 5 ) 4 ) 1 ) 4 ) 5 8 19. (a) No, f ( x ) 5 } x x 2 1 2 1 1 } is discontinuous at x 5 2 1. (b) } x x 2 1 2 1 1 } 5 x 2 1, x 2 1 The area between the graph of f and the x -axis over [ 2 2, 1) where f is negative is } 1 2 } (3)(3) 5 } 9 2 } . The area between the graph of f and the x -axis over (1, 3] where f is positive is } 1 2 } (2)(2) 5 2.
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