Find the area of the region bounded by the graphs of y = 2 − x2 and y = −x.Find the area of the region bounded by the graphs of y = 2 − x2 and y = −x.

Answer 1

Make a sketch.
We will need to know where they intersect
-x = 2-x^2
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 or x = -1
height of region = 2-x^2 - (-x)
= 2+x-x^2

area = ∫(2+x-x^2)dx from -1 to 2
= [2x + (1/2)x^2 - (1/3)x^3] from -1 to 2
= ...

I will leave the arithmetic for you