I assume you are looking for the area. A straightforward integration will give the algebraic area, since the curves cross at x=1, and the area changes sign.
∫[-2,2] (-x^2+6x+2)-(2x^2+9x-4) dx
= ∫[-2,2] -3x^2-3x+6 dx
= 8
However, to get the geometric area, you need to split the region into two parts:
∫[-2,1] (-x^2+6x+2)-(2x^2+9x-4) dx + ∫[1,2] (2x^2+9x-4)-(-x^2+6x+2) dx = 27/2 + 11/2 = 19
Between y = 2x2 + 9x − 4 and y = −x2 + 6x + 2 for x in [−2, 2]
1 answer