Science:Math Exam Resources/Courses/MATH101/April 2012/Question 07 (c)/Statement

Let $I=\int _{1}^{2}(1/x)\,dx$. Without computing I, find an upper bound for $|I-S_{4}|$. You may use the fact that if $|f^{(4)}(x)|\leq K$ on the interval $[a,b]$, then the error in using S_n to approximate $\int _{a}^{b}f(x)\,dx$ has absolute value less than or equal to $K(b-a)^{5}/180n^{4}$.