 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/undated/prelims/mathematics-iii-resit/3/b/i/solution

r (t) = (t, t, t)

0 \leq t \leq 1

. Then

F (r (t)) = (t, t^{2}, t)

and

r^{'} (t) = (1, 1, 1)

\int_{C} F \cdot d r = \int_{0}^{1} (2 t + t^{2}) d t = \frac{4}{3} .

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