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lana [24]
4 years ago
15

Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by:

Mathematics
1 answer:
natali 33 [55]4 years ago
8 0

The volume is

\displaystyle2\pi\int_0^2x^3\,\mathrm dx=\frac\pi2 x^4\bigg|_0^2=8\pi

Each shell has a height of x^2 (distance between y=x^2 and y=0) and width equal to the distance to the axis of revolution (x-0=x), hence contributing a surface area of 2\pi x^3. Sum (integrate) over all x in the region of interest to get the volume.

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