 Solution

ID: past-exam-of-the-numerical-analysis-course-of-the-university-of-oxford/2017/1/d/iii/solution

q = 4

Q (g) = \frac{1 + 1/4}{36} = \frac{5}{144}, I (g) = \frac{1}{30} .

This is an overestimate, with signed quadrature error

Q (g) - I (g) = \frac{25 - 24}{720} = \frac{1}{720} .

(1/720) / (1/30) = 1/24

, approximately

4.17%

y^{4}

lies beyond the degree of precision of a quadrature rule of Simpson's rule, so the exactness of the previous cases no longer applies.

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