 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/i/solution

h = (b - a) / n

and

x_{i} = a + ih

. Summing the areas of the

n

endpoint trapezia gives the composite trapezoidal rule

T_{n} = h [\frac{f ( x _{0} ) + f ( x _{n} )}{2} + i = 1 \sum n - 1 f (x_{i})] .

Every interior value is shared by two adjacent strips; the two endpoint values occur only once with half weight. Evenness of

n

is not needed for this rule.

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