Module 4: Numerical Integration

Overview

In engineering, there are times the integral value is needed of an equation or of a dataset. Numerical integration can be divided into two different branches:

  1. 1. Integrating to find the area under a set of data.
  2. 2. Integrating to find the area under an equation.

Integrating under a dataset is useful in experiments when the total value of a system is desired. For example, if the concentration of a species is taken at multiple points of a reactor, integrating over that space would yield the mass of the species. This can generally be completed using the family of Newton-Coates integrators. Integration of equations can sometimes be completed analytically, but oftentimes the equations are complex to integrate, or do not have an analytical solution. In these cases, using efficient methods such as Romberg Integration or Gauss Quadrature are most useful.

Learning Objectives

At the end of this module, you will be able to:

  • NI|LO|01: Identify a numerical integration problem.
  • NI|LO|02: Solve dataset based numerical integration problems.
  • NI|LO|03: Solve equation-based numerical integration problems.

Knowledge Test

Before you jump into the module, complete this test to learn what concepts you will learn in this module.