How do you find the area between the curves #y=4x-x^2# and #y=x#?
First, we need to find where the two functions intersect.
So our interval of integration is
The integral for the area is
integrating we have
Evaluating at we have
Find the points of intersection,
then subtract from the integral of the first (between
the integral of the second (again, between
Points of intersection occurs when
This occurs when either
(we could, but don't actually need to calculate