A fast way to compute definite integrals

Bogdan-Cãlin Ciobanu, Florin Pop, Pantelimon George Popescu

Abstract: In this paper, we present a fast method to compute definite integrals using triangles to approximate the area beneath a function. This method achieves the same result as the composite trapezoidal rule, but faster. We analyze the method’s performance, comparing it with other integration methods, specifically the functions from Computer Algebra Systems, such as Wolfram Mathematica, QUADPACK and Matlab, and show that this method outperforms those implementations. Numerical experiments are included to confirm its performance gain.