How do you find the area of the region bounded above by the parabola y=2-x^2, and below by the line y=-x' ?

1 Answer
May 14, 2018

Use the form:

"Area" = int_a^b f_2(x)-f_1(x) dx, f_2(x) > f_1(x)

Explanation:

We know that f_2(x) = 2-x^2 and f_1(x) = -x

"Area" = int_a^b 2-x^2-(-x) dx

Find the values of a and b by setting the right sides of the two equations equal:

-x = 2-x^2

x^2-x-2=0

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

x = -1 and x = 2

This means that a = -1 and b = 2

"Area" = int_-1^2 2-x^2+x dx

"Area" = 2x-1/3x^3+1/2x^2|_-1^2

"Area" = 2(2)-1/3(2)^3+1/2(2)^2-(2(-1)-1/3(-1)^3+1/2(-1)^2)

"Area" = 9/2