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!