Question

Use cylindrical shell method to find the volume of the solid obtained by rotating the region bounded by the given curves x^2=y and y^2=x about y=-1?

Answer 1

Please see below.

Explanation:

Volume of a slice is `2pirh"thickness"`

In this case:
`r = y+1`
`h = sqrty-y^2`
`"thickness" = dy`

`y` varies from `0` to `1`.

So the volume is

#V = int_0^1 2pi(y+1)(sqrty-y^2)dy = 2pi[29/60] = (29pi)/30#