Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
y^2=x, y=1, x=0
Hello,
I've used curvature's diagram to show you where you can find those cylindrical shells: see attachment.
One shell is calculated by:
$\displaystyle s=2 \pi y \cdot x$ Substitute $\displaystyle x = y^2$ into this equation and you'll get:
$\displaystyle s = 2 \pi y^3$
Now sum up all shells between the given bounds and you get the volume of the solid:
$\displaystyle V = \int_0^1 2 \pi y^3 dy = \left. \frac{1}{2} \pi y^4 \right|_0^1 = \frac{1}{2} \pi$