# Riemann Sum A Riemann sum is an approximation of the area under a curve, done by splitting the area into $n$ rectangles of the same width. The sum is then known as the $n$-approximation of the area. The limit of the sum as $n$ goes to 0 is then the actual [[Integral]]. $R_f(a,b, n) = \frac {b-a} {n}\sum_{j=0}^{n-1} f \left(a+j\frac {b-a}n \right)$ ^q211no $\int \limits_a^b f(x) dx = \lim_{n \to \infty} R_f(a,b,n)$ ^zrxo9z