Numerical Approximation of Integrals using Multi-Segment Trapezoidal Rule

by Tyler Riedal

Submitted : Fall 2013

This project is intended to explore the accuracy of numerical solving methods when compared to analytical solving methods. Three integral problems were chosen as support for the project’s thesis. Each of these integral problems require different methods to solve analytically; specifically, integration by parts, U-substitution, and trigonometric integral solving methods. After solutions are obtained via numerical and analytical methods, the solutions are compared in a convergence of integral graph. From the graphs it can be concluded that in some instances it is more efficient to use numerical solving methods because it is nearly as accurate as analytical solving methods and less time consuming. A fourth example is included as a counterexample showing to show instances where analytical methods are more efficient than numerical methods.

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