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

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

(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

$|E_M|\le \frac{K(b-a{)}^3}{24n^2}\text{and}|E_S|\le \frac{L(b-a{)}^5}{180n^4},$

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