PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Student interpretation and justification of “backward” definite integrals
Page: 1275
The definite integral is an important concept in calculus, with applications throughout mathematics and science. Studies of student understanding of definite integrals reveal several student difficulties, some related to determining the sign of an integral. Clinical interviews of 5 students gleaned their understanding of “backward” definite integrals, i.e., integrals for which the lower limit is greater than the upper limit and the differential is negative. Students initially invoked the Fundamental Theorem of Calculus to justify the negative sign. Some students eventually accessed the Riemann sum appropriately but could not determine how to obtain a negative quantity this way. We see the primary obstacle here as interpreting the differential as a width, and thus an unsigned quantity, rather than a difference between two values.