Question

Let S be the region bounded by the graphs of \sqrt{x}, e^{-2x}, and the vertical line x=1.

a. Find the area of S

b. Suppose S is revolved around the line x=1. Using the cylindrical shell method, find an integral expression equal to the volume of the solid that is created.

c. Now suppose S is the base of a solid. For that solid, each cross section perpendicular to the x-axis is a rectangle with height 5 times the length of the base region S. Find the volume of this solid.




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Answer #1

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