Calculate the area of the figure that is bounded by the graph of the function y = x ^ 2-x-6 and the abscissa.

Let’s find the points of intersection of the graph of the given function with the abscissa axis:

x ^ 2 – x – 6 = 0

x12 = (1 + – √ (1 – 4 * 6)) / 2 = (1 + – 5) / 2

x1 = -2; x2 = 3

The area S of the figure limited by the graph will be equal to:

S = ∫ (x ^ 2 – x – 6) * dx | -2; 3 = (1/3 * x ^ 3 – 1/2 * x ^ 2 – 6x) | -2; 3 =

9 – 4.5 – 18 – 8/3 – 2 + 12 = 14/3.