# What is the volume of the solid produced by revolving f(x)=x^2, x in [0,4] around the x-axis?

Feb 12, 2017

Volume $= \frac{1024 \pi}{5} \setminus {\text{unit}}^{3}$

#### Explanation:

graph{(y-x^2)=0 [-4.5, 4.5, -2, 18]}

The Volume of Revolution about $O x$ is given by:

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

So for for this problem:

$V = {\int}_{0}^{4} \setminus \pi {\left({x}^{2}\right)}^{2} \setminus \mathrm{dx}$
$\setminus \setminus \setminus = \pi \setminus {\int}_{0}^{4} \setminus {x}^{4} \setminus \mathrm{dx}$
$\setminus \setminus \setminus = \pi \setminus {\left[\frac{{x}^{5}}{5}\right]}_{0}^{4}$
$\setminus \setminus \setminus = \frac{\pi}{5} \setminus {\left[{x}^{5}\right]}_{0}^{4}$
$\setminus \setminus \setminus = \frac{1024 \pi}{5}$