# Math Help - Area of Region

1. ## Area of Region

#1.)

Find the are of the region bounded by
y= 1 divided by x^2, y=x, and y=8x, for x>0

2. Originally Posted by loutja35
#1.)

Find the are of the region bounded by
y= 1 divided by x^2, y=x, and y=8x, for x>0
make a sketch

find the intersection x-values ...

$\frac{1}{x^2} = 8x$ at $x = \frac{1}{2}$

$\frac{1}{x^2} = x$ at $x = 1$

$x = 8x$ at $x = 0$

set up the integral expressions ...

$
A = \int_0^{\frac{1}{2}} 8x - x \, dx + \int_{\frac{1}{2}}^1 \frac{1}{x^2} - x \, dx
$