Find the area (in square units) of the region under the graph of the function f on the interval [−1, 2].

Question

Find the area (in square units) of the region under the graph of the function f on the interval [−1, 2].

f(x)=-x^2+5

Answer 1

Area A = ∫_-1²(- x² + 5)dx =(- x³/3 + 5x)_-1² = (- 8/3 + 10) - (1/3 - 5) = 15 - 3 = 12.