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Problem 20 Medium 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 + y^2) \textbf{i} + xz \textbf{j} + (y + z) \textbf{k} $,
$ \textbf{r}(t) = t^2 \textbf{i} + t^3 \textbf{j} - 2t \textbf{k} $, $ 0 \leqslant t \leqslant 2 $

Answer

8

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Video Transcript

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