ON A STUDY OF ERROR BOUNDS OF TRAPEZOIDAL RULE
Nahmwoo Hahm, Bum Il Hong · Honam Mathematical Journal · 2014
In this paper, through a direct computation with subintervals partitioning [0, 1], we compute better a posteriori bounds for the average case error of the difference between the true value of $I(f)=\int_{0}^{1}f(x)dx$ with $f{\in}C^r$ [0, 1] minus the composite trapezoidal rule and the composite trapezoidal rule minus the basic trapezoidal rule for $r{\geq}3$ by using zero mean-Gaussian.