Strips between two curves

You will write a small program that adds thin strips between two curves, and compare it with the shortcut for a parabola cut by a line. The checker uses a line and a parabola, two parabolas, and the shortcut.

The idea. A strip at $x$ has height $f(x) - g(x)$, where $f$ is the upper curve. Add many strips of width $dx$. The shortcut for a parabola with $x^2$ coefficient $a$, cut by a line at $x_1$ and $x_2$, is $\dfrac{|a|\,(x_2 - x_1)^3}{6}$.

Your tasks.

1. Finish strip_height(f, g, x). Return the height of the strip at x, the upper curve f minus the lower curve g.
2. Finish area_between(f, g, a, b). Use 2000 strips of equal width between a and b, and the middle of each strip.
3. Finish segment_area(a, x1, x2). Return the shortcut area.