 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/16/b/ii/solution

y = 1 + z

, the integrand is

x + z + z^{2}

\iint_{S} (x + yz) d S = 2 \int_{0}^{2 π} \int_{0}^{1} (x + z + z^{2}) d z d x = 2 \int_{0}^{2 π} (x + \frac{5}{6}) d x = 2 (2 π^{2} + \frac{5 π}{3}) .

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