Originally Posted by

**Archie Meade** No, Tweety,

When you are dealing with the area between curves as in your case,

with one below the other, you can subtract the functions first,

then integrate.

Subtract the lower curve from the upper curve.

$\displaystyle 4x-x^2-(x^2-4x)=8x-2x^2.$

now you can integrate the difference between them

and that gives the area.

Notice that $\displaystyle 4x-x^2$ is $\displaystyle x^2-4x$ upside down.

Hence the area above the x axis between the points of intersection,

is always positive there.

Hence integrating that will give a positive answer.

Then double your answer since that will give you the area.

Or, integrate the lower curve, but since that one is negative, your answer

will be negative.

So just change the sign and multiply by 2.

If you do all 3 ways, it would be excellent practice.