1. ## Integrals - Volume

Question:
The region in the first quadrant bounded by the graphs f(x)=(1/8)(x)^3 and g(x)=2x is rotated about the y-axis. Find the volume of the solid formed.

I know the integral basics.
I think I have to place the y points and I think I am meant to convert the y= into x= so I have a x equation.

This is what I got after integrating etc.

((6144/50)*(pi))-((512/12)*pi)).
This I guess is not right.
Thanks for any help.

2. Originally Posted by Awsom Guy
Question:
The region in the first quadrant bounded by the graphs f(x)=(1/8)(x)^3 and g(x)=2x is rotated about the y-axis. Find the volume of the solid formed.
using washers ...

$V = \pi \int_0^8 (2\sqrt[3]{y})^2 - \left(\frac{y}{2}\right)^2 \, dy
$

using cylindrical shells ...

$V = 2\pi \int_0^4 x \left(2x - \frac{x^3}{8}\right) \, dx$

3. Then I guess I do the normal Solving the function by subbing in the x values. thanks.