[Math] Find the volume of the solid generated when the region enclosed..

Question

Find the volume of the solid generated when the region enclosed
$$y= \sqrt {x+1},\ y= \sqrt {2x},\ y=0$$
is revolved about the $x$-axis.

I found that both curves only have one intersection at $x=1$. How can I proceed then?

Answer 1

I assumed the following colored are is supposed to revolve about $x$ axis.:

$x=1$ gives $y=\sqrt{2}$, so we have $$V=2\pi\int_{y=0}^{\sqrt{2}}y(x_2-x_1)dy$$ where $y^2-1=x_2,~~\frac{y^2}{2}=x_1$.