Based on the closed interval, continuous functions in the definite integral to study mathematics knowledge based on analysis of numerical analysis of composite trapezoidal formula and XinFuSheng formula for the ideological basis, using C programming language tool design procedure. The definite integral and continuous function after the related definitions, discusses the two algorithm using C language, and write the corresponding program. The algorithm is verified through a function for the correctness and rationality, and discussed the two algorithm in scope and accuracy of the differences in slightly. Finally, through this exposition promotion to the other for the realization of the definite integral of the algorithm
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