Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x−8x^2,

Question

xenn [34]

2 years ago

14

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x−8x^2,

y = 0; about the y-axis.

Mathematics

1 answer:

Mandarinka [93] · Answer 1 · 2022-07-10T20:02:08+03:00

Mandarinka [93]2 years ago

4 0

We need to get the limits first. When y = 0
0 = 64x - 8x^2
x = 0 and x = 8
The volume is
V = ∫ y dx from 0 to 8
V = ∫ (64x - 8x^2) dx from 0 to 8
V = 32x^2 - 8x^3/3 from 0 to 8
V = 682.67<span />