#1.)

Find the are of the region bounded by

y= 1 divided by x^2, y=x, and y=8x, for x>0

Printable View

- Sep 10th 2009, 08:03 AMloutja35Area 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 - Sep 10th 2009, 12:11 PMskeeter
make a sketch

find the intersection x-values ...

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

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

$\displaystyle x = 8x $ at $\displaystyle x = 0$

set up the integral expressions ...

$\displaystyle

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

$