Trapezoidal Rule:

If is continuous on then may be approximated as: where a and b are limits of integration and n is the number of intervals.

Simpson’s Rule

If is continuous on then may be approximated as:

where a and b are limits of integration and n is the number of intervals.

This tutorial deals with the numerical techniques of integration. Methods such Simpson’s Rule and the Trapezoidal Rule are discussed in this tutorial. The idea o finding the area of complex shapes is covered in this tutorial. The trapezoidal rule is discussed in some of the examples.

Simpson’s Rule is covered in this tutorial as a second numerical method for evaluating integrals that would otherwise be difficult to calculate by pen and paper. Mathematical programs exhibit the graphs of the solutions to integrals discussed in this tutorial.

Specific Tutorial Features:

• Step by step examples showing the numerical techniques of integration.
  
• Simpson’s rule and the Trapezoidal rule are covered with the aid of visual based examples

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  
• Definition slides introduce terms as they are needed.
  
• Visual representation of concepts
  
• Animated examples—worked out step by step
  
• A concise summary is given at the conclusion of the tutorial.

The trapezoidal rule
 Examples of how to use the trapezoidal rule
Simpson’s Rule 
  Examples of how to use Simpson’s rule