find the volume by rotating about x-axis

**yoman360** · October 19th 2009, 06:50 PM

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

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

I tried this and got the wrong answer.

**WhoCares357** · October 19th 2009, 06:58 PM

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

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

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

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

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