Science:Math Exam Resources/Courses/MATH101/April 2016/Question 9 (b)/Solution 1
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Here , the derivatives of which are
For , the functions and attain their maximum values at . Thus,












 ,











and












 .











Consequently, for the Midpoint Rule with :
whereas for Simpson’s Rule with :
Therefore, the fact that implies that Simpson’s Rule results in a smaller error bound.