 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-2/2/solution

The integrand is an even function, since both

x

and

sin x

\int_{- π /2}^{π /2} x sin x d x = 2 [- x cos x + sin x]_{0}^{π /2} = 2 .

The endpoint cosine terms vanish, leaving the sine contribution.

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