Originally Posted by

**x0ne** I need to find the area of the curve between 2 functions:

$\displaystyle y= x^2$ and $\displaystyle y= 2x-x^2$

Taking the integral of both is easy:

$\displaystyle \frac{1}{3}x^3$ and $\displaystyle x^2-\frac{1}{3}x^3$

At this point I know I need to find the intersects of the functions so I can then find the definitive integral.

I begin the process like so:

$\displaystyle x^2=2x-x^2$

Then:

$\displaystyle 2x-x^4$

Then:

$\displaystyle 2x(1-x^3)$

At this point I think I am just having a brain spaz as I don't know how to get the 2 points I need so I can plug them into the functions. Am I doing something wrong and in general, do I have the correct idea?