longoriamariah5020 longoriamariah5020
  • 18-04-2018
  • Mathematics
contestada

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 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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