Science:Math Exam Resources/Courses/MATH101/April 2016/Question 09 (b)/Statement

Both parts of this question concern the integral $I=\int _{0}^{2}(x-3)^{5}\,dx$.

(b) Which method of approximating $I$ results in a smaller error bound: the Midpoint Rule with $n=100$ intervals, or Simpson’s Rule with $n=10$ intervals? Justify your answer. You may use the formulas

$|E_{M}|\leq {\frac {K(b-a)^{3}}{24n^{2}}}\qquad {\text{and}}\qquad |E_{S}|\leq {\frac {L(b-a)^{5}}{180n^{4}}},$

where $K$ is an upper bound for $|f''(x)|$ and $L$ is an upper bound for $|f^{(4)}(x)|$.