Calculate the area of the curved trapezoid bounded by the lines y = -x ^ 2 + 9 and the abscissa.

Find the intersection points of the parabola with the oX axis, for this we equate the equation to 0:

– x ^ 2 + 9 = 0;

x ^ 2 = 9;

x = + – 3.

The area S of the formed figure will be equal to the integral:

S = ∫ (9 – x ^ 2) * dx | -3; 3 = (9x – 1/3 * x ^ 3) | -3; 3 = 9 * 3 – 1/3 * 3 ^ 3 – (9 * (-3) – 1/3 * (-3) ^ 3) = 54 – 2/3 * 3 ^ 3 = 54 – 18 = 36.