Find the area between the following curves y1= x2−4x+3 y2=−x2+2x+3

Answer 1

The curves intersect at (0,4) and (3,0)

area = ∫[0,3] (-x^2+2x+3) - (x^2-4x+3) dx
= ∫[0-3] 6x - 2x^2 dx
= 3x^2 - 2/3 x^3 [0,3]
= 9