Overview
The Riemann integral was one of the first and simplest integrals to be defined. An integral is a method that is designed to try to calculate the area underneath a curve.For example, consider the area underneath the following curve.
Properties
The Riemann integral is known to have the following properties.
Linearity
{% {\displaystyle \int }_a^b c_1f(x)+ c_2g(x) dx = c_1{\displaystyle \int }_a^b f(x) dx + c_2{\displaystyle \int }_a^b g(x) dx %}
Additivity
{% {\displaystyle \int }_a^b f(x) dx + {\displaystyle \int }_b^c f(x) dx = {\displaystyle \int }_a^c f(x) dx %}
Riemann Lower Sum
The Riemann lower sum approximates the integral by calculating the area of the rectangles below the curve for the given mesh size.Number of Divisions
Riemann Upper Sum
The Riemann upper sum approximates the integral by calculating the area of the rectangles above the curve for the given mesh size.Number of Divisions