A major source of anxiety for engineering and science majors who must take calculus is the topic of integration. The techniques of integration necessary for solving practical problems in the sciences are lengthy and complex. In this paper, we are introducing a method that minimizes the algebra as well as the number of computations for certain types of integrals. It is important to note that we are not suggesting that the conventional methods for teaching techniques of integration be replaced with the innovation we are proposing. Rather, the new approach we suggest is to be presented only after the traditional techniques of integration by parts and substitution have been taught. The new approach is called the probability density function (p.d.f .) method and uses the properties of probability density functions to evaluate integrals for certain classes of functions. In this paper we demonstrate that, for certain classes of functions, this method greatly reduces the length and complexity of many integration problems.
Pitman, Stacy and Lazari, Andreas
"Using Well-Known Probability Density Functions to Evaluate Certain Integrals in Calculus,"
Georgia Journal of Science, Vol. 64, No. 2, Article 2.
Available at: https://digitalcommons.gaacademy.org/gjs/vol64/iss2/2