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.

Author Bio

Daniel Pietz has been an undergraduate student at Embry-Riddle Aeronautical University in Prescott Arizona since Fall of 2018. will graduate in Spring 2021 with Bachelor’s degrees in Computer Engineering with a focus in robotics, and Software Engineering. After graduating, he intends to pursue a PhD in computational mathematics. The submitted work was completed during September 2018 - March 2019 under the supervision of Dr Christopher Briggs, Assistant Professor of Mathematics at Embry-Riddle Aeronautical University.