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Chapter 10
Simpson's Rules for
areas and centroids
Areas and volumes
Simpson's Rules may be used to ®nd the areas and volumes of irregular ®gures. The rules are based on the assumption that the boundaries of such ®gures are curves which follow a de®nite mathematical law. When applied to ships they give a good approximation of areas and volumes. The accuracy of the answers obtained will depend upon the spacing of the ordinates and upon how near the curve follows the law.
Simpson's First Rule
This rule assumes that the curve is a parabola of the second order. A parabola of the second order is one whose equation, referred to co-ordinate axes, is of the form y a0 a1x a2x2, where a0, a1, and a2 are constants.
Let the curve in Figure 10.1 be a parabola of the second order. Let y1, y2 and y3 be three ordinates equally spaced at `h' units apart.
Fig. 10.1
