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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
$$
\int_{C} \mathbf{F} \cdot d \mathbf{r}=0
$$
Topics
Vector Calculus
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Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Catherine R.
Missouri State University
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Baylor University
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Idaho State University
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Video Transcript
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Topics
Vector Calculus
Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Catherine R.
Missouri State University
Caleb E.
Baylor University
Michael J.
Idaho State University
