1. ## Finding the volume

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.x = 5 + y2, x = 0, y = 1, y = 2

I am unsure how to tackle this one.
I tried rearranging the above equation to y^2=x-5 and the obtaining the necessary x values at the above y values, these were 9 and 6. So then i did the integral from 9 to 6 of pi multiplied by x-5 and this came out to be incorrect.

2. ## Re: Finding the volume

I always draw a sketch...this makes things clear...

The volume of an arbitrary shell is given by:

$\displaystyle dV=2\pi y(y^2+5)\,dy$

Hence:

$\displaystyle V=2\pi\int_1^2 y^3+5y\,dy$