 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/6/c/ii/solution

With the same three cosine values, Simpson's rule gives

S_{2} = \frac{π}{12} (1 + \frac{4}{2} + 0) = \frac{π}{12} (1 + 22) = 1.002279 \dots = 1.002 .

Using the table's

n = 12

row gives

0.2618 + 4 (0.1851) = 1.0022

, with the same final rounding. That table row refers to the prefactor

π /12

; it does not change the specified number of strips.

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