 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/13/a/ii/solution

For

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

(2 t, 1)^{T}

and

F (r (t)) = (t^{3}, t^{4} + t)^{T}

. Thus

\int_{0}^{1} (2 t^{4} + t^{4} + t) d t = \frac{3}{5} + \frac{1}{2} = \frac{11}{10} .

The unequal values for the same endpoints already rule out a conservative vector field.

 New to topics? Read the docs here!