ABSTRACT
A problem that frequently arises in engineering applications is that of integration of a given function f(x) over a speci˜ed range of the independent variable x. In many cases, the function f(x) is continuous, ˜nite, and well behaved over the range of integration a ≤ x ≤ b, where a and b are constants. Then, the integral I where
I f x x a
= ( )∫ d
(8.1)
may often be determined by using available mathematical or analytical techniques. The results for common elementary functions such as sin x, cos x, ex, x2, 1/x, and so on, are well known, and those for many more complicated functions are given in integral tables. Symbolic algebra available in MATLAB®, Mathematica, Maple, and other such environments may also be used in many cases to obtain the integral analytically. Analytical, or closed-form, expressions for integrals, whenever available, are of considerable value since they are exact, that is, without the errors that inevitably arise in numerical methods. Moreover, they are generally applicable over given domains without any limitations, so that the effect of varying the physical parameters, associated with the problem, on the integral may easily be investigated. In addition, analytical results can be employed in the validation of a numerical integration scheme and for estimating the accuracy of the results.
