# find the volume by rotating about x-axis

• Oct 19th 2009, 06:50 PM
yoman360
find the volume by rotating about x-axis
use the graph to find approximate x-coordinates of the points of intersection of the given curves. then find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves

$\displaystyle y=x^2$
$\displaystyle y=\sqrt{x+1}$

I tried this and got the wrong answer.
• Oct 19th 2009, 06:58 PM
WhoCares357
Quote:

Originally Posted by yoman360
use the graph to find approximate x-coordinates of the points of intersection of the given curves. then find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves

$\displaystyle y=x^2$
$\displaystyle y=\sqrt{x+1}$

First you find the bounds.
$\displaystyle x^2=\sqrt{x+1}$ (I used a graphing calculator to find the two intersections).
$\displaystyle x_1=-.724492; x_2=1.2207441$

You know that area of a circle is $\displaystyle \Pi r^2$.
Then you set up the integral.
$\displaystyle \Pi\int^{x_2}_{x_1} (\sqrt{x+1}^2-(x^2)^2)dx$