 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/12/c/solution

I_{0, 1} (π /2, 0) = 1

I_{3, 1} (π /2, 0) = \frac{9}{10} \frac{6}{7} \frac{3}{4} = \frac{81}{140} .

Each factor corresponds to reducing

n

by one; the final unreduced integral is just

\int_{0}^{π /2} cos u d u = 1

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