 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-2/3b/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Parametrize the straight segment by

x = t

y = 1 + t

0 \leq t \leq 1

. The line integral becomes

\int_{0}^{1} [t^{2} - (1 + t) + (1 + t)^{2} + t] d t = \int_{0}^{1} (2 t^{2} + 2 t) d t = \frac{5}{3} .

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