Find the Area of the Shape Bounded by Lines y = x ^ 2 + 3 y = 0 x = -1x = 1

The quadratic function does not intersect the Ox axis and is limited to the indicated straight lines. The area to be calculated is equal to the integral of the quadratic function, the lower limit is -1, the upper limit is 1, i.e .:

s = integral (-1 to 1) (x² + 3) dx = x³ / 3 + 3 * x (-1 to 1) = 1/3 + 3 + 1/3 + 3 = 2/3 + 6 = 20/3 units ².

Answer: the required figure has an area equal to 20/3 units ².