SOLUTION: I need help with this problem: Find the area of the region completely enclosed by the graphs of y = {{{x^2}}} -2 and y = x.

Algebra ->  Finance -> SOLUTION: I need help with this problem: Find the area of the region completely enclosed by the graphs of y = {{{x^2}}} -2 and y = x.      Log On


   

Question 1026291: I need help with this problem:
Find the area of the region completely enclosed by the graphs of y = x%5E2 -2 and y = x.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I need help with this problem:
Find the area of the region completely enclosed by the graphs of y = x%5E2+-+2 and y = x.
------------
Find the 2 points of intersection.
x%5E2+-+2+=+x
x%5E2+-+x+-+2+=+0
x = -1 and x = 2
----------
f(x) = x%5E2+-+x+-+2+=+0
F(x) = x%5E3%2F3+-+x%5E2%2F2+-+2x Ignore the constant of integration.
Area = F(2) - F(-1)
= (8/3 - 2 - 4) - (-1/3 - 1/2 + 2)
= (-10/3) - (7/6)
= -27/6
Area = ABS = 4.5 sq units