Question

The region between the graphs of y=x^2 and y=6x is rotated around the line x=6.
The volume of the resulting solid is ?

Answer 1

h(x) = f(x) - g(x) = x² - 6x
Vol.Rotate = 2*Pi * Integral( h(x)² ) dx

Answer 2

1. Find their intersection points.
=> Put y=x^2 into y=6x => x(x-6)=0 => x=0 or x=6
2. \[ volume=2π \int_{0}^{6} (6-x)(6x) - (6-x)(x^2) dx\]
Can you do it from here?
(PS: I'm not sure if it is correct :S)

Answer 3

Yup I got it from here, Thanks a lot!

Answer 4

Welcome :)
Note: This time, I still use shell method to do it..