Area between curves

To find the area between curves, follow these steps:

1. Rough sketch: There can be other tasks needed to complete this step, review the following: Absolute value:

$$\begin{array}{r}|A|=\{\begin{array}{rlr}& A& A\ge 0\\ & -A& A<0\end{array}\end{array}$$

2. Finding parabola’s vertex: for

$$y=f(x)=a{x}^2+bx+c$$ $$x=-\frac{b}{2a}$$

2. Find the intervals: where do the curves intersect?
3. Find the area using integrations

If finding the area by integrating with x (or in my word “moving along the x-axis) requires more intervals or is too difficult to do, you may use integrating with y.