Math Help - Volume by shell method

1. Volume by shell method

I'm trying to find the volume of this set of values

y=x^3
y=8
x=0

it is being rotated about the x-axis, the back of my text gives an answer of 768* pi/7 however i dont seem to be getting this value

2. Originally Posted by XyxFibonaccixyX
I'm trying to find the volume of this set of values

y=x^3
y=8
x=0

it is being rotated about the x-axis, the back of my text gives an answer of 768* pi/7 however i dont seem to be getting this value

method of washers ...

$V = \pi \int_0^2 8^2 - (x^3)^2 \, dx$

3. Im wondering why it is that you have 8^2 - (x^3)^2

and also what would this look like if it were a method of shells,

4. Originally Posted by XyxFibonaccixyX
Im wondering why it is that you have 8^2 - (x^3)^2

method of washers ...

$\textcolor{red}{V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx}$

and also what would this look like if it were a method of shells

$\textcolor{red}{V = 2\pi \int_0^8 y \cdot \sqrt[3]{y} \, dy}$
...