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Area, Volume, and Arc Length

Area, Volume, and Arc Length

Example 1

Find the volume of the solid generated when the region bounded by ex and the x-axis on the interval [0,1] is rotated around the y-axis, using

(a) the washer method

(b) the shell method

Example 2

Let R be the region bounded by the graph y = 2xx2 and the x axis.

(a) Sketch the solid obtained by rotating R around the y-axis.

(b) Is it easier to use washers or shells to find the volume of the solid you drew in (a)? Why?

(c) Write an integral expression for the volume of the solid you drew in (a).

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