# What is the surface area produced by rotating f(x)=1/(x+1), x in [0,3] around the x-axis?

Jun 22, 2016

$\frac{3 \pi}{4}$

#### Explanation:

Revolvong a small elemental area about the x axis creates volume of revolution $\Delta V = \pi {y}^{2} \Delta x$

The volume therefore is

$V = \pi {\int}_{0}^{3} {y}^{2} \setminus \mathrm{dx} = \pi {\int}_{0}^{3} \setminus \frac{1}{x + 1} ^ 2 \setminus \mathrm{dx}$
$= \pi {\left[- \frac{1}{x + 1}\right]}_{0}^{3} = \pi {\left[\frac{1}{x + 1}\right]}_{3}^{0}$
$= \pi \left(1 - \frac{1}{4}\right) = \frac{3 \pi}{4}$