Problems solving in the integral calculus and the determination of the area under the curve

Abstract

In Integral Calculus the classic problem is the determination of the area under the curve, when said region is not expressible in terms of elementary figures. This translates into a multiplicity of problems and exercises that are presented to students in a Calculus course. This article presents a useful problem for Mathematics Education, derived from a generalized integral operator, for this we define what we understand by an integrable function in this generalized sense, and the geometric interpretation of a generalized definite integral is presented. The interesting thing about this generalization is that said geometric interpretation is similar to the geometric interpretation of the classical Riemann integral, but not in the xy plane, but in the Ty plane, where T is the kernel of the generalized integral.

Keywords

• Problems solving
• integral calculus
• area under the curve