As the question asks find the Area of the region enclosed by

Solution

x^2-4*x=-x^2+4*x 2*x^2=8*x x=0,4 so these are the endpoints. Just subtract bottom curve from top curve integral from 0 to 4 of -x^2+4*x-(x^2-4*x) integral from 0 to 4 of -2*x^2+8*x -2/3*x^3+4*x^2 from 0 to 4 -2/3*64+4*16 1/3*64 A=64/3=21.333