Q:

Area of the region enclosed by $y=x^2-1$, $y=2x-1$, and $y=x+1$

Find the area of the region enclosed by $y=x^2-1$, $y=2x-1$, and $y=x+1$.
Like the question I asked before, I still do not understand how to find these areas.

A:

Find the intersection of $y=x^2-1$ and $y=x+1$.
$x^2-x-2=0$
$x=-1,2$
$$S1=\int_{-1}^2\left[x+1-\left(x^2-1\right)\right]dx$$
Find the intersection of $y=x^2-1$ and $y=2x-1$
$x^2-2x=0$
$x=0,2$
$$S2=\int_0^2\left[2x-1-\left(x^2-1\right)\right]dx$$
What does $S1-S2$ give you?
fast answer posted due to desmos 'misc' function.

