Riemann Sums

The core operations of the Calculus are "infinite subtraction" (or differentiation) and "infinite summation" (or integration). In the latter realm, we can leverage a discretized version which uses Riemann Sums.

When it comes to a bunch of basic shapes like rectangles, circles, and triangles, we have simple formulas to compute their areas.

We know that for a rectangle with sides of length $a$ and $b$, the area is just the product $a\cdot b$, for circles it's $\pi r^2$ and triangles use $\frac{1}{2} b\cdot h$.

Suppose we have the function $f(x) = x^2$ and we want to compute the area between interval $0$ and $1$.