Question

How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis `y=7x^2`, x =1, y =0, about the x-axis?

Answer 1

Volume = `(49pi)/5`

Explanation:

A small portion of the volume
`dV=piy^2dx`
Where dx is the thickness
so `V=int_a^bpiy^2dx`
`V=int_0^1pi(7x^2)^2dx`
`V=piint_0^1(49x^4)dx`
`V=pi((49x^5)/5)` from `x=0` to `x=1`
`V=pi49/5-0`