Riemann Integral
Overview
The Riemann integral was one of the first and simplest integrals to be defined.
Definition
The integral
{% \int_a^b f(x)dx %}
is defined as the
limit
of a sum
{% \int_a^b f(x)dx = lim_{\Delta x \rightarrow 0} \sum_{i=1}^{n-1} f(x_i) (x_{i+1} - x_i) %}
where the interval {% [a,b] %} is split into subintervals as [{% x_1, x_2, ... , x_n %}]
where {% x_1 = a %} and {% x_n = b %}
