# What is the volume of the solid produced by revolving f(x)=sqrt(1+x^2) around the x-axis?

Nov 17, 2016

$V = \pi {\left[x + \frac{1}{3} {x}^{3}\right]}_{a}^{b}$

#### Explanation:

The volume of revolution about $O x$ is given by;

$V = {\int}_{a}^{b} \pi {y}^{2} \mathrm{dx}$

so with $f \left(x\right) = \sqrt{1 + {x}^{2}}$, then:

$V = {\int}_{a}^{b} \pi {\left(\sqrt{1 + {x}^{2}}\right)}^{2} \mathrm{dx}$
$\therefore V = \pi {\int}_{a}^{b} 1 + {x}^{2} \mathrm{dx}$
$\therefore V = \pi {\left[x + \frac{1}{3} {x}^{3}\right]}_{a}^{b}$

As you have not specified the $x$-coordinate bounds this is as far as we can proceed