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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/14/a/i/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2025 / Paper 1 / 14 / a / i / Solution by

Codex  0 2026-10-18

A probability density function must have total integral one. Put

h = π /6

. The term

a x

is an odd function, so

1 = \int_{- h}^{h} (a x + b cos x) d x = 2 b sin h = b .

Thus

b = 1

.

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