Is Simpson's Rule Applicable to Finding Volume and Area?

[z37002]

1)how do you set up simpsons rule for volume, if its NOT rotated about exactly on the axis?
2)can you use simpsons rule for shells method?
3)an example?

Homework Equations

v=integral 2pie(radius)(height)dx
change of x\n\3 14241

The Attempt at a Solution

nc

 

[LCKurtz]

Whether the integral represents volume by shells or disks, or area, or anything else, it doesn't matter. You will have some integral of the form $\int_a^b f(x)\, dx$. Just use the formula for Simpson's rule using $a$ and $b$, the number of intervals $n$ and your formula $f(x)$, whatever it is. You do know the Simpson rule formula, right?