Analysis of the Area Under a Curve (AUC) using C-programming: Trapezium and Simpson rules techniques.

Abstract

This study aimed to analyze the Area Under a Curve (AUC) using C-programming i.e. Trapezium and Simpson rules. There are various mathematical methods that can be applied to solve numerical integration for different data spaces. Among them are the Trapezium and Simpson rules which are widely used to solve numerical integration equations. The objective of this study was to study the calculation of the area under the curve more accurately and to identify the error differences between the Trapezium and Simpson rules in the calculation of the area under the curve. In addition, it also compares the fit between the Trapezium and Simpson rules. This study focuses on identifying methods that provide more accurate values in the area below the curve. C-programming study utility to verify the accuracy of area calculations under the curve between Trapezium and Simpson rules. The results showed a difference of 6.93% in the area under the curve for calculations using C-programming based on the Trapezium rule compared with the exact calculations. Meanwhile, a calculation difference of 6.23% was recorded for the Simpson rules. In general, the data show that the Simpson rules obtained a relatively low difference of 0.623 when compared to the Trapezium rule which yielded a value of 0.693 which means that the Simpson rule has a more accurate estimate value for AUC calculation using C- programming when compared to the Trapezium rules.

Keywords

• c-programming
• trapezium and simpson rules
• area under a curve