Find the volume of the solid revolved around y=x^3, y=0, x=2 about the y-axis

Answer 1

Answer 2

1) Draw the region on 2-d

notice region is in quadrant 1. And since we are revolving around y axis

we need to write these two functions which bound the region in relation

1) y(x)=x^3 ---> y^1/3 = x

2) x=2

Formulate expression right - left AKA DISH-WASHER METHOD

2 - y^1/3

A(y) = pi( expression) ^2

A(y) = pi(2)^2 - pi(y^2/3)

To find volume integrate A(y) where the bound a and b are y values of endpoint thus from [0 8] since they intersect at 8.

thus

V = integral A(y) from 0 to 8 dy

V= pi * int (A(y),0,8,dy)

V= 64*pi/5 =

V= 40.21238 units cubed