Question

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.

Answer 1

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`