Answer
TRUE
Work Step by Step
True; Because the starting and ending points are the same, by the fundamental theorem for line integrals, $\int_C \nabla f \cdot d \mathbf{r} = f(\mathbf{r}(a)) - f(\mathbf{r}(a)) = 0$.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.