Other Mathematics Commons^™

Numerical Integration Through Concavity Analysis, Daniel J. Pietz

Rose-Hulman Undergraduate Mathematics Journal

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.