# What is the volume of the solid produced by revolving f(x)=1/x, x in [1,4] around the x-axis?

Apr 1, 2018

$\frac{3 \pi}{4}$ units""^3

#### Explanation:

Volume of revolution about the $x$ axis is given by, $V = \pi \int {y}^{2} \mathrm{dx}$, where $y$ is a function of $x$

In this case $y = f \left[x\right]$=$\frac{1}{x}$, so $V = \pi \int {\left[\frac{1}{x}\right]}^{2} \mathrm{dx}$.

$\frac{1}{x} ^ 2$ can be written as ${x}^{-} 2$, this can be integrated using the general power rule, intx^ndx=x^[n+1]/[n+1 , giving $\int \frac{1}{x} ^ 2 \mathrm{dx} = - \frac{1}{x}$

Therefore the volume will $= \left[- \frac{\pi}{4}\right] - \left[- \frac{\pi}{1}\right] = \frac{3 \pi}{4}$ units""^3