Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves x=4y2−y3 and x=0 about the x-axis.

Question

asked Mar 14, 2021 65.7k views

1 Answer

Morleyc · Answer 1 · 2021-03-18T17:10:57+0000

Answer = 321.7

Step-by-step explanation:

radius = y

height =
4y^(2) - y^(3)

area of cylinder = 2π*r*h

Integrate the area to calculate the volume:

$= \int\limits^0_4 {2\pi(4y^(3) -y^(4)) } \, dy$

$= 2\pi (\int\limits^0_4 {4y^(3)dy -\int\limits^0_4 y^(4) dy )} \,$

$= 2\pi (256-(1024)/(5) )$

$=(512\pi )/(5)$

= 321.7