Question

How do you find the volume of the solid obtained by rotating the region bounded by `y=x` and `y=x^2` about the line `x=-1`?

Answer 1

By Shell Method,

`V=2pi int_0^1(x+1)(x-x^2)dx=2pi int_0^1(x-x^3)dx`

`=2pi[x^2/2-x^4/4]_0^1=2pi(1/2-1/4)=pi/2`

---

I hope that this was helpful.