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# Area, Volume, and Arc Length

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# Washers vs. Shells Exercises

### Example 1

Find the volume of the solid generated when the region bounded by *e ^{x}* 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* = 2*x* – *x*^{2} 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).