Find area of the region enclosed

Question

Calculate the area of the region enclosed by the parabola 𝑦 = 2 - 𝑥² and 𝑦 = -𝑥

Answer 1

set 2-x^2 = -x

x^2-x -2 = 0

(x-2)(x+1) = 0

the parabola and line intersect at (2,-2) and (-1,1)

integral of 2-x^2 +x = -(1/3)x^3 +(1/2)x^2 +2x

evaluate at 2

-(1/3)8 + 2 + 4= 18/3 - 8/3 = 10/3

evaluate at -1

1/3 +1/2 -2 = -12/6 +2/6+3/6 =-7/6

subtract

10/3 - (- 7/6) = 27/6= 4.5