Question

use the method of cylindrical shells to find the volume v of the solid obtained by rotating the region bounded by the given curves about the x-axis. y = x3, y = 27, x = 0

Answer 1

To find the volume using the method of cylindrical shells, we integrate the difference between the height and radius of each shell.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves y = x^3, y = 27, and x = 0 about the x-axis, we can use the method of cylindrical shells.

We need to express the volume as an integral with respect to x. The radius of each shell is given by x, and the height of each shell is given by the difference between 27 and x^3. Therefore, the volume V is given by the integral:

V = ∫[0,3] (2πx(27 - x^3)) dx