ABSTRACT
This chapter provides students to use the trapezoidal rule, mid-ordinate rule, and Simpson's rule to determine irregular areas. It also provides students to estimate the volume of irregular solids and determine the mean values of waveforms. There are many applications in business, economics and the sciences, including all aspects of engineering, where finding the areas of irregular shapes, the volumes of solids, and the lengths of irregular shaped curves are important applications. Engineers need to concern themselves with issues of geotechnical engineering and with quantity estimation to ensure that soil volumes in the cuts match those of the fills, while minimizing the distance of movement. Simpson's rule is a staple of scientific data analysis and engineering; it is widely used, for example, by naval architects to numerically determine hull offsets and cross-sectional areas to determine volumes and centroids of ships or lifeboats.
