computing integrals by simplifying the right hand side of ( we get zb xdx oef xn xn /( which is more compactly written as zb xdx xi xn ( composite integration rules the word composite is often used when numerical integration method is applied with more than one sub-interval strictly speaking thenwritinge "the trapezoidal method"should imply the use of only single trapezoidwhile "the composite trapezoidal methodis the most correct name when several trapezoids are used howeverthis naming convention is not always followedso saying just "the trapezoidal methodmay point to single trapezoid as well as the composite rule with many trapezoids implementation specific or general implementationsuppose our primary goal was to compute the specific integral /dt with td first we played around with simple hand calculation to see what the method was aboutbefore we (as one often does in mathematicsdeveloped general formula ( for the general or rb "abstractintegral /dx to solve our specific problem /dt we must then apply the general formula ( to the given data (function and integral limitsin our problem although simple in principlethe practical steps are confusing for many because the notation in the abstract problem in ( differs from the notation in our special problem clearlythe xand in ( correspond to vtand perhaps for the trapezoid width in our special problem the programmer' dilemma should we write special program for the special integralusing the ideas from the general rule ( )but replacing by vx by tand by should we implement the general method ( as it stands in general function trapezoid(fabnand solve the specific problem at hand by specialized call to this functionalternative is always the best choicethe first alternative in the box above sounds less abstract and therefore more attractive to many neverthelessas we hope will be evident from the examplesthe second alternative is actually the simplest and most reliable from both mathematical and programming point of view these authors will claim that the second