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Problem 22 Hard Difficulty

Evaluate the line integral $ \displaystyle \int_C \textbf{F} \cdot d \textbf{r} $, where $ C $ is given by the vector function $ \textbf{r} (t) $.

$ \textbf{F}(x, y, z) = x \textbf{i} + y \textbf{j} + xy \textbf{k} $,
$ \textbf{r}(t) = \cos t \textbf{i} + \sin t \textbf{j} + t \textbf{k} $, $ 0 \leqslant t \leqslant \pi $

Answer

$$
\int_{C} \mathbf{F} \cdot d \mathbf{r}=0
$$

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Video Transcript

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