Find the volume of the solid obtained by rotating the region bounded by y = 8 x 2 , x = 1 , and y = 0 , about the x -axis.

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18-04-2018
Mathematics

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Find the volume of the solid obtained by rotating the region bounded by y = 8 x 2 , x = 1 , and y = 0 , about the x -axis.

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JцstinBieber JцstinBieber · Answer 1 · 2018-04-22T00:19:31+02:00

JцstinBieber JцstinBieber

22-04-2018

A cross-section is a disc with radius [tex]8x^2[/tex]

[tex]V = \int_0^1 A(x)\, dx = \int_0^1 \pi\left(8x^2\right)^2 dx = \int_0^1 64 \pi x^4 = \left[\frac{64\pi}{5} x^5\right]_0^1 \\ \\ = \frac{64\pi}{5} [/tex]

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