A02 - x = 1. 4. A cylinder of radius b is inserted through...

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Math 138 – Fall 2011 Assignment 2 Due Friday September 30 (in the drop box by 12 noon) Hand in the following: 1. Compute Z x 3 + 1 x 2 - 2 x + 5 dx 2. (a) Find Z 1 1 - x 2 dx (b) Use the result in (a) to derive Z sec( x ) dx = ln | sec( x ) + tan( x ) | + C Hint: Note that sec( x ) = 1 cos( x ) = cos( x ) cos 2 ( x ) 3. Consider the region in the xy plane bound by the curves x = 2 ,x = 4 , y = 0 and y = x . Find the volume of the solid that is obtained when this region is rotated about the line
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Unformatted text preview: x = 1. 4. A cylinder of radius b is inserted through the center of a sphere of radius a ( a > b ). Find the volume that lies outside the cylinder but inside the sphere. (Another way to think of it is to assume the sphere is like an apple and you are coring the apple (radius a ) with a cylinder (radius b ) and determining the volume of what remains)....
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