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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The solution is a detailed explanations of the application of integral on finding the volume of solid generated by revolving around a horizontal line.