ABSTRACT
There are plenty of examples where irregular areas and volumes need to be determined by engineers. Area of irregular plane surfaces may be approximately determined by using a planimeter, and Simpson's rule. Such methods may be used, for example, by engineers estimating areas of indicator diagrams of steam engines, surveyors estimating areas of plots of land or naval architects estimating areas of water planes or transverse sections of ships. This chapter aims to determine the mean values of waveforms and volume of irregular solids. 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. The chapter explains the trapezoidal rule and the mid-ordinate rule to determine irregular areas.
