# How do you find the area between #f(x)=-x^2+4x+2, g(x)=x+2#?

##### 1 Answer

We start by finding the intersection points of the two functions.

#{(y = -x^2 + 4x + 2), (y = x+ 2):}#

#x+ 2 = -x^2 + 4x + 2#

#x^2 - 3x = 0#

#x(x - 3) = 0#

#x = 0 and 3#

#y = 0 + 2 and y = 3 + 2#

#y = 2 and y= 5#

Hence, the intersection points are

We now do a rudimentary sketch of the two functions.

We always proceed in the following way: AREA BETWEEN CURVES = AREA OF CURVE ABOVE - AREA OF CURVE BELOW. We find this area using integration.

We will subtract the area under

Hence, the area between the curves is

Hopefully this helps!