Pre-Calc Homework Solutions 304

Pre-Calc Homework Solutions 304 - 304 30 Section 7.3 35 1 4...

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30. [ 2 1, 4] by [ 2 1, 3] A cross section has radius r 5 y 3/2 and area A ( y ) 5 p r 2 5 p y 3 . The volume is E 2 0 p y 3 dy 5 p 3 } 1 4 } y 4 4 5 4 p . 31. [ 2 1.2, 3.5] by [ 2 1, 2.1] Use washer cross sections. A washer has inner radius r 5 1, outer radius R 5 y 1 1, and area A ( y ) 5 p ( R 2 2 r 2 ) 5 p [( y 1 1) 2 2 1] 5 p ( y 2 1 2 y ). The volume is E 1 0 p ( y 2 1 2 y ) dy 5 p 3 } 1 3 } y 3 1 y 2 4 5 } 4 3 } p . 32. [ 2 1.7, 3] by [ 2 1, 2.1] Use cylindrical shells: a shell has radius x and height x . The volume is E 1 0 2 p ( x )( x ) dx 5 2 p 3 } 1 3 } x 3 4 5 } 2 3 } p . 33. [ 2 2, 4] by [ 2 1, 5] Use cylindrical shells: A shell has radius x and height x 2 . The volume is E 2 0 2 p ( x )( x 2 ) dx 5 2 p 3 } 1 4 } x 4 4 5 8 p . 34. [ 2 0.5, 1.5] by [ 2 0.5, 1.5] The curves intersect at x 5 0 and x 5 1. Use cylindrical shells: a shell has radius x and height ˇ x w 2 x . The volume is E 1 0 2 p ( x )( ˇ x w 2 x ) dx 5 2 p 3 } 2 5 } x 5/2 2 } 1 3 } x 3 4 5 } 2 1 p 5 } . 35.
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