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Let R be the shaded region bounded by the graphs of y=sqaure root of x, and y=e to the power of -3x, and the vertical line x=1.

Let R be the shaded region bounded by the graphs of y=sqaure root of x, and y=e to the power of -3x, and the vertical line x=1.  
a) Find the area R
b) Find the volume of the solid generated when R is revolved about the horizontal line y=1.
c) The region R is the base of a solid.  For this solid, each cross section perpendicular to the x-axis is a rectangle whose height is 5 times the length of its base region R.  Find the volume of this solid.
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This question was asked on Apr 25, 2010.

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