Calculate the area of a flat figure bounded by lines y = x ^ 3 + 2, y = x-2, x = 2.

Let’s find the point of intersection of the given functions, for this we equate their formulas:

x ^ 3 + 2 = x – 2;

x ^ 3 – x – 4 = 0;

x = 1.8.

The area of the figure S will be equal to the difference of the integrals:

S = ∫ (x ^ 3 + 2) * dx | 1.8; 2 – ∫ (x – 2) * dx | 1.8; 2 = (1/4 * x ^ 4 + 2x) – (1/2 * x ^ 2 – 2x) | 1.8; 2 = (12 – 3.9) – (- 2 – 1.98) ≈ 12.