# Area Between the Curve...

• May 21st 2009, 06:27 PM
Foreman.
Area Between the Curve...
This is probably simple for you guys, but ive been having problems with this one...

Y=abs(x) and y=x^2-2

I can integrate it once i have it set up but im having trouble remembering how to find the limits of integration and set up the basic problem. Can anyone help?
• May 21st 2009, 08:03 PM
TheEmptySet
Quote:

Originally Posted by Foreman.
This is probably simple for you guys, but ive been having problems with this one...

Y=abs(x) and y=x^2-2

I can integrate it once i have it set up but im having trouble remembering how to find the limits of integration and set up the basic problem. Can anyone help?

See the graph.

Attachment 11529

So the area is

$\displaystyle 2\int_{0}^{2}x-(x^2-2)dx$
• May 23rd 2009, 02:06 PM
Foreman.
Okay I understand most of it now.

Just one thing, why do we multiply the entire equation by 2?
• May 23rd 2009, 02:09 PM
e^(i*pi)
Quote:

Originally Posted by Foreman.
Okay I understand most of it now.

Just one thing, why do we multiply the entire equation by 2?

TheEmptySet integrated between 0 and 2. However, there is also a part from -2 to 0. Since this is a reflection of the positive part then it will have the same area so the total area is twice the integral