Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (b)/Hint 1

The difference between the integral and the midpoint rule of order 6 will at most be the error, given by the formula above. To bound the 2nd derivative of $f(x)=x\sin x$ on $[0,\pi ]$ use the inequalities

$|x+y|\leq |x|+|y|,\,|\cos x|\leq 1,\,|\sin x|\leq 1$.

Note you do not need to calculate the midpoint rule approximation.