 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/i/solution

Two strips give

h = π /4

, with cosine values

1, 1/ 2, 0

. The trapezoidal rule therefore gives

T_{2} = \frac{π}{8} (1 + 2) = 0.948059 \dots = 0.948 .

The exact integral is

1

, so the estimate is low, consistent with the concavity of cosine on this interval. The table can be used as

T_{2} = \frac{1}{2} (0.7854) + 0.5554

before rounding.

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