Question

How do you find the volume of a solid that is enclosed by `y=x^2`, `y=0`, and `x=2` revolved about the x axis?

Answer 1

The volume is `=(32pi)/5`

Explanation:

A unit slice has a volume

`dV=pi*y^2*dx`

As, `y=x^2`

`dV=pix^4dx`

We use, `intx^n=x^(n+1)/(n+1)+C (n!=-1)`

Therefore,

`V=int_0^2pix^4dx=pi[x^5/5]_0^2`

`V=pi*32/5`