Find the area of the figure bounded by the graph of the function y = (x-2) ^ 2, y = 0, x = 0

Find the point of intersection of the given curve with the oX axis:

x – 2 = 0;

x = 2.

Then the area S of the figure formed by the coordinate axes and the given curve will be determined by the integral:

S = ∫ (x – 2) * dx | 0; 2 = ∫x * dx | 0; 2 – ∫2 * dx | 0; 2 = x ^ 2/2 | 0; 2 – 2x | 0; 2 = (2 ^ 2/2 – 2 ^ 0/2) – (2 * 2 – 2 * 0) = 4 – 4/3 = 8/3.

Answer: the area of the figure formed by the given graphs is 8/3.