Abstract
This chapter describes two methods of numerical integration in naval architrcture: trapezoidal and Simpson's rule. The rules are exemplified on integrands defined by explicit mathematical expressions. this is done to show that the two methods of numerical integration are efficient and to allow an evaluation of errors. It uses the geometrical approach to derive the two most popular rules, namely the trapezoidal and Simpson's rules. These two methods are sufficient for solving most problems encountered in Naval Architecture. The error terms will be given without derivation. The trapezoidal rule approximates the given curve by a straight line segments, while Simpson's rule approximates it by a parabola. It is possible to show convincingly that the approximations yield satisfactory results. Naval architecture requires the calculation of areas, moments of areas, moments of inertia of areas, volumes and moments of volumes. Such calculations involve definite integrals. Usually the hull surface is defined by line drawings or tables of offsets, and not by explicit mathematical expressions. The integrals can be obtained only by numerical methods.
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