Double integrals in engineering mathematics: Confusing region geometry with integrands

In engineering mathematics, double integrals are encountered in a wide range of fields, such as electrodynamics, aerodynamics and quantum mechanics. Setting up appropriate bounds and integrands is key to successfully solving an integral; computation is often easy, by hand or with software. In a recent study within a multivariable calculus course for Electrical Engineering, Applied Physics and Advanced Technology majors, we investigated students’ proficiency at setting up double integrals to represent the area of a two-dimensional region provided in a diagram. In the case of computing an area, the integrand should be unity, yet we found that a significant portion of the students created an integrand out of the bounds of the region. One identical error was incurred by sixty percent of those cases. In this paper we present the different classes of incorrect integrands, how students relate to the geometry of the region and discuss potential causes. In particular, we observe that when using a single variable to calculate area under a curve, the integrand is not unity, which might cause cognitive conflict. We discuss implications for the teaching and learning of double integrals and suggest educational interventions.