Answer
True.
Work Step by Step
Because the starting and ending points are the same, by the fundamental theorem for line integrals, $\int_C \nabla f \cdot d \mathbf{r} = f(\mathbf{r}(a)) - f(\mathbf{r}(a)) = 0$.
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 16 - Vector Calculus - Review - True-False Quiz - Page 1160: 4
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