Design of integral spreadsheet calculator for engineering applications

Abstract

AbstractAlthough Newton‐Cotes integration formulas in engineering have been the subject of the study for a long time, the improvement in formulations is still object of interest. In this sense, design of calculators based on these formulations becomes significant. The purpose of this paper is to design an integral calculator for any engineering problems. Since the integral calculator, easy‐to‐understand and use, is aimed to be employed by any kind of users. Visual Basic for Applications (VBA) is the programming language of Excel. Excel spreadsheet with VBA is preferred for this purpose. In this study, a user interface input form is introduced. This form is composed of the embedded algorithm. This algorithm includes not only rules and formulations of each Newton‐Cotes such as Composite Trapezoidal rule, Simpson's rules, Boole's rules, and Gauss Legendre formulations with 2, 6, 10, 16, and 24 points and exact result of any integral (if it exists) with computed true percent relative error for comparison purposes. This calculator is tested for civil, mechanical, and chemical engineering applications. The results and screenshots for each application obtained from calculator are presented. The present study allows design of an integral spreadsheet calculator for any integral given. If exact result of the integral cannot be obtainable, the calculator can perform only integral calculations numerically without exact solution and computed true percent relative error. Otherwise, user can solve the integrals completely with this tool easily and accurately again but this time by both numerically and analytically with true percent relative error calculations.