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m_a_m_a [10]
3 years ago
14

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.

Mathematics
1 answer:
pashok25 [27]3 years ago
6 0
A cross-section is a disc with radius 8x^2

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}
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