Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line.

Question

y = x3
y = 0
x = 3

the x-axis,the y-axis,and the line x = 4

Answer 1

I will assume your curve is y = x^3

first part:
Volume = π∫y^2 dx from 0 to 3
= π∫x^6 dx from 0 to 3
= π[(1/7)x^7] from 0 to 3
= π(2187/7 - 0) = 2187π/7

2nd part
(you will need x = .... from y = x^3
x^3 = y
x = y^(1/3)

vol = π∫(3 - y^(1/3) )^2 dy from y = 0 to y = 27
expand, then integrate etc.