# Area of Region

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• September 10th 2009, 09:03 AM
loutja35
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
• September 10th 2009, 01:11 PM
skeeter
Quote:

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
$