# Integration problem(simple)

• May 14th 2006, 07:21 AM
Jones
Integration problem(simple)
Hi, how do do if i want to calculate the area limited by three functions.
Say i have the three funtions Y=x, y=8x and y=1/x^2
• May 14th 2006, 08:01 AM
CaptainBlack
Quote:

Originally Posted by Jones
Hi, how do do if i want to calculate the area limited by three functions.
Say i have the three funtions Y=x, y=8x and y=1/x^2

You break the range of integration down into regions bounded by only
two of the curves and a vertical line.

In the example you give we have:

$
Area=\int_{x=0}^{\frac{1}{\sqrt{2}}} \int_{y=x}^{8x} \ dy\ dx\ +
\int_{x=\frac{1}{\sqrt{2}}}^{1} \int_{y=x}^{\frac{1}{\sqrt{x}}} \ dy\ dx
$

RonL