 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/b/ii/solution

For the same uniform grid and even

n

, the composite Simpson's rule integrates a quadratic interpolant over each successive pair of strips:

S_{n} = \frac{h}{3} f (x_{0}) + f (x_{n}) + 4 j = 1 \sum n /2 f (x_{2 j - 1}) + 2 j = 1 \sum n /2 - 1 f (x_{2 j}) .

The weights are

1, 4, 2, 4, \dots, 2, 4, 1

, which explains the even number of strips.

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