 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/8/a/solution

Reflection in the

y

-axis preserves the disk but changes the sign of the integrand

x y

. The double integral is therefore its own negative and must be

0 .

Equivalently, for each fixed

y

x

on a symmetric interval.

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