IMPROVED FORM OF SIMPSON’S ONE-THIRD RULE FOR FINDING APPROXIMATE VALUE OF DEFINITE INTEGRALS BY USING TRIGONOMETRIC FUNCTIONS

C. V. Rao Department of General Studies (Mathematics), Jubail Industrial College, Jubail Industrial City, Kingdom of Saudi Arabia, cvrao@jic.edu.sa

Abstract

Numerical integration plays an important role in various fields of science and engineering. Existing numerical integration methods are midpoint rule, Trapezoidal rule, Simpson's rule, Rom berg's and Boole's rule. In this paper I have derived a new form of numerical integration by using the condition on the integrand f(x) satisfies the condition f(x_i )=∅(x_i ),i=0,1,2…n where ∅(x)=〖A cos〗⁡x+B sin x+Cx. For this method I choose n value so that step size h is sufficiently small. As far as novelty of the paper is concern, fewer calculations taken into account with enough preciseness and results are in agreement with Simpson’s one-third rule.

Keywords:

Numerical integration; Trigonometric functions; Quadratic polynomial; Simpson's rule; Trapezoid’s rule; approximations.


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References



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