Numerical Integration Formulæ

Chapter

Abstract

In ships and other floating structures calculation of section areas, waterplane areas, volumes and various properties such as first and second moments is commonplace. This leads to the evaluation of integrals of the form seen in the previous Chap.  5, for example,
$$ A = 2\;\int \limits _{x_A }^{x_F } {y(x)\;dx ,} $$
$$ M_x = 2\;\int \limits _{x_A }^{x_F } {x\;y(x)\;dx ,} $$
$$ J_{xx} = 2\;\int \limits _{x_A }^{x_F } {x^2 y(x)\;dx ,} $$
$$ a(x) = 2\;\int \limits _{_0 }^T {y(z, x)\;dz ,} $$
$$ \nabla = \;\int \limits _{x_A }^{x_F } {a(x)\;dx ,} $$
etc.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

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