We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.
Dr. Christopher Briggs
Pietz, Daniel J.
"Numerical Integration Through Concavity Analysis,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 21
, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss2/7