 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-v/2/b/i/solution

r (t) = (t, t^{2}, t^{3})

0 \leq t \leq 1

F (r (t)) = (9 t^{2}, - 14 t^{5}, 20 t^{7}), r^{'} (t) = (1, 2 t, 3 t^{2}) .

Consequently the line integral is

\int_{C} F \cdot d r = \int_{0}^{1} (9 t^{2} - 28 t^{6} + 60 t^{9}) d t = 3 - 4 + 6 = 5.

 New to topics? Read the docs here!