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
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Ruch, Dave, "The Definite Integrals of Cauchy and Riemann" (2017). Analysis. 11.