Definite Integral for Real Life Problem Solving in Science and Engineering: An Overview

Definite integral is used to calculate length of curves, areas and volumes. It is also used to calculate mass of a body of varying density, displacement, velocity, acceleration, projectile motion and vertical motion of a ball or object. Work done by a variable force, potential energy, total gravitational force, and total kinetic energy of a rotating rod can be obtained by methods of definite integral. Applications of definite integrals are also found in probability computation using probability density function, fluid pressure, finding the mean age and median age of a group of cells, rate of growth, rate of decay and consumption over time, and calculating the minimum costs and maximum profits in economics. They are used to also solve many interesting problems in finance. They however have wide range of applications in engineering, sciences and management, and hence the need to review, assess and evaluate research work put forward to improve means of solving it, in order to point out gaps, that will trigger more contributions to the definite integral research trend. Researchers in the field of mathematics, computer science and engineering are able to provide definite integral solvers in the form of websites, software like MATLAB and MAPLE, Algorithm such as firefly and Neural Network, Calculators with incorporated functionality to solve definite integrals and some device an enhanced manual methods to provide easier means of solving definite integrals when compared with the conventional or traditional methods. The paper assessed definite Integral solvers on websites, software packages, algorithms, devices available to solve definite integrals and research trends aimed at solving definite integral, and identified more contributions that are needed in each category of the solvers. Conclusions are drawn and appropriate recommendations were made to further improve definite integral solvers, to meet up with constant change in technologically driven global village and for overall success in numerous application areas.

Keywords:

Definite Integrals , Integral Solvers , Algorithms and Gaps