 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/17/c/iii/solution

Start with the supplied Gaussian integral

I (0) = π /2

and part (i)'s

I (1) = 1/2

. Repeated use of the Gaussian moment recurrence gives

I (2) = \frac{π}{4}, I (3) = \frac{1}{2}, I (4) = \frac{3 π}{8}, I (5) = 1, I (6) = \frac{15 π}{16} .

The even indices inherit the

π

factor from

I (0)

, while the odd indices inherit rational values from

I (1)

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