Pre-Calc Homework Solutions 320

Pre-Calc Homework Solutions 320 - 320 25. Chapter 7 Review...

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25. [ 2 1, 2] by [ 2 1, 2] Use washer cross sections. A washer has inner radius r 5 1, outer radius R 5 e x /2 , and area p ( R 2 2 r 2 ) 5 p ( e x 2 1). The volume is E ln 3 0 p ( e x 2 1) dx 5 p 3 e x 2 x 4 5 p (3 2 ln 3 2 1) 5 p (2 2 ln 3). 26. Use cylindrical shells. Taking the hole to be vertical, a shell has radius x and height 2 ˇ 2 w 2 w 2 w x w 2 w . The volume of the piece cut out is E ˇ 3 w 0 2 p ( x )(2 ˇ 2 w 2 w 2 w x w 2 w ) dx 5 2 p E ˇ 3 w 0 2 x ˇ 4 w 2 w x w 2 w dx 5 2 p 3 2} 2 3 } (4 2 x 2 ) 3/2 4 52} 4 3 } p (1 2 8) 5 } 28 3 p } < 29.3215 ft 3 . 27. The curve crosses the x -axis at x 56 3. y 952 2 x , so the length is E 3 2 3 ˇ 1 w 1 w ( w 2 w 2 w x ) w 2 w dx 5 E 3 2 3 ˇ 1 w 1 w 4 w x 2 w dx , which using NINT evaluates to < 19.4942. 28. [ 2 2, 2] by [ 2 2, 2] The curves intersect at x 5 0 and x 56 1. Use the graphs’ x - and y -axis symmetry: } d d x } ( x 3 2 x ) 5 3 x 2 2 1, and the total perimeter is 4 E 1 0 ˇ 1 w 1 w ( w 3 w x 2 w 2 w 1 w ) 2 w dx , which using NINT evaluates to
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