# How do you find the area between #f(x)=x+1# and #g(x)=(x-1)^2#?

##### 1 Answer

The area is

#### Explanation:

Start by finding the intersection points of the curves.

#{(y = x+ 1), (y = (x - 1)^2):}#

Solve by substitution.

#x + 1= (x- 1)^2#

#x+ 1 = x^2 - 2x + 1#

#0 = x^2 - 3x#

#0 = x(x - 3)#

#x= 0 and 3#

We now draw the two curves to see which one is *above* and which one is *below.* This is important, as we will then find the area under the higher curve and subtract the area of the lower curve.

So, we find the area of the linear function (

Hopefully this helps!