# How do you find the area between the curves #y=4x-x^2# and #y=x#?

##### 2 Answers

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,

between

then subtract from the integral of the first (between

the integral of the second (again, between

**Part 1:**

Points of intersection occurs when

This occurs when either

(we could, but don't actually need to calculate

**Part 2:**

with

this becomes