+129850 y = 2x - 6 = 2 ( x - 3)
y = x^3 - 2x^2 - 3x = x ( x - 3) ( x +1)
Intersection points
x ( x - 3) (x + 1) = 2 (x - 3)
x ( x - 3) (x + 1) - 2(x - 3) = 0
(x - 3) (x^2 + x - 2) = 0
(x - 3) ( x + 2) ( x - 1) = 0
We have three ontersection pts x = -2 x = 1 and x = 3
See the graph here : https://www.desmos.com/calculator/1l3ht5pza6
We have two areas to consider
1 3
∫ (x^3 -2x^2 - 3x) - (2x - 6) dx + ∫ (2x - 6) - (x^3 - 2x^2 - 3x) dx =
-2 1
1 1 1 1 1 3 3 3
[ (1/4)x^4 ] - [(2/3)x^3] - [(3/2)x^2 ] - [x^2] + [6x] + [ x^2] - [6x] - [ (1/4)x^4] +
-2 -2 -2 -2 -2 1 1 1
3 3
[ ((2/3)x^3] + [ (3/2)x^2 ] =
1 1
-15/4 -6 + 9/2 + 3 + 18 + 8 -12 -20 + 52/3 + 12 = 253 / 12
