Question

Can you help me please? Find the area of the region between the curves y=abs(x) and y=(x^2)-2

Answer 1

Start with the limits of integration for the integral. For the limits of integration, we find where \[\left| x \right|=x^{2}-2\]

Answer 2

I would take advantage of the symmetry with the y axis. Both equations are symmetric with respect to the y axis.

Answer 3

They intersect at x=-2 and x=2, so we do:\[\int\limits_{-2}^{2}(\left| x \right|-(x ^{2}-2))dx\]
abs(x) is first because abs(x)>x^2-2

Answer 4

on that interval

Answer 5

And yeah we could do it from 0 to 2 and multiply that by 2

Answer 6

okay, so I integrated from 0 to 2 and then multiplied by 2 to find the area on the other side. My final answer was 20/3 and it was correct. Thank you both so much!

Answer 7

Sure