Calculate the area of the figure bounded by lines y = 4-x ^ 2; y = 0.

first you need to solve the equation y = 4 -x ^ 2 where y = 0

4 – x ^ 2 = 0

4 = x ^ 2 the solution to the equation will be the roots x1 = 2 x2 = -2

since we have a quadratic equation, the graph of the function will be a parabola, the branches of the parabola are directed downward.

To calculate the area of the figure, it is necessary to integrate the function: y (x) = 4 – x ^ 2 over d (x). The limits of this function are the roots of the equation x1 and x2 we found.

integral = AND

И = 4 x – (x ^ 3) / 3- according to the table of integrals

И = И (x2) – И (x1) we substitute

S = And (2) – And (-2) = (8 – 8/3) – (-8 + 8/3) = 16 – 16/3 = 32/3 = 10.666666- the area of the figure

Answer: S = 10.666666