Utilizing Integrals and Simpson’s Rule to Determine Displacement of Particle

by Kyle Hayes

Submitted : Spring 2021

The aim of this project was to, given the velocity equation of a particle to begin, use two different methods to obtain the displacement of the particle. Utilizing integration was one method, through a use of u-substitution and integrals by parts the original equation could be integrated. Solving the definite integrals then gives us the displacement of the particle. The second method to be utilized is Simpson’s Rule. This equation needs to be solved two times as we are given two different n terms in the beginning to utilize (n = 4, 6). Then, the values from all equations are then compared. In the end, the average value found from the equations was about 174.8. What this value means is that the particle was displaced by about 174.8 meters in 12 seconds. Overall, the purpose of this project is to compare two similar techniques, and see how close the approximate gets to the actual integration, and to understand what that value means in terms of that equation.

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