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

Question

anonymous · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

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

anonymous · Answer

on that interval

anonymous · Answer

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

tiffany_rhodes · Answer

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!

anonymous · Answer

Sure