# Modified Integration with MAPLE

### Wei-Chi Yang

Department of Mathematics & Statistics
USA
Phone: (540) 831-5232
Fax: (540) 831-6452

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## ABSTRACT

It has been known that computer algebra system such as Maple can be used to help students learning and researchers making new mathematical conjectures. In this paper, I will demonstrate how we could make use the symbolic and numeric computation capacity of Maple and infinite matrices to integrate a monotone function with singularity such as f(x) =1/sqrt(x) if x is not equal to 0 and f(0) = 0. Traditional methods such as Riemann sum, trapezoid, and Simpson's rules usually divide interval into equally spaced subintervals. But for a function such as f it is more efficient to divide the interval [0,1] unevenly, say smaller to the left than to the right, because the function is steeper to the left. We shall also look at the case when a function is highly oscillating, such as f(x) = (1/x)*sin(1/x) for x is in (0,1], and f(0) = 0. We will see how the infinite matrices together with the trapezoidal rule are implemented in Maple without using the method of transformation.

Being the chair of the international program committee, I will also preview the First Asian Technology Conference in Mathematics, Singapore, December 18-21, 1995.

Keyword(s): Maple, calculus, integrals