Calculate the area of the shape bounded by the lines y = (x + 2) ^ 2, y = 0, x = 0.

univerkov | April 15, 2021 | education

Find the intersection points of the curve y = (x + 2) ^ 2 with the abscissa:

(x + 2) ^ 2 = 0;

x + 2 = 0;

x = -2.

Then the area S of the figure bounded by the given lines will be equal to:

S = ∫ (x + 2) ^ 2 * dx = 1/3 * (x + 2) ^ 3 | -2; 0 = 1/3 * 2 ^ 3 – 1/3 * (-2 + 2) ^ 3 = 8/3 – 1/3 = 7/3.

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