In addition to looking at the percent errors of different methods for integrating, our group also wanted to explore the effectiveness of the various methods for different types of functions. We were guided to explore an example of trigonometric, linear, quadratic, and cubic functions, but wanted to see if patterns emerged within these different types of functions and ultimately if a particular method of integration gives more accurate estimations given a specific type of function.
The actual data we collected, or a detailed summary of the data can be seen here. From this data we found that Simpson’s method is by far the best method of the five methods we explored, particularly for cubic functions. For symmetric functions such as trigonometric functions as well as quadratic functions, the midpoint method is also very accurate. Trapezoidal method provides an accurate estimation especially for small deltas, but has trouble with cubic formulas. The other Reimann sum methods provide over or underestimates depending on the type of function but, especially for larger deltas, are not as accurate as the other methods.