Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.
Applicable Math Courses
analysis, advanced calculus
Upper Division Undergraduate
Ruch, Dave, "The Definite Integrals of Cauchy and Riemann" (2017). Analysis. 11.