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Problem 24 Hard Difficulty

Use a calculator to evaluate the line integral correct to four decimal places.

$ \displaystyle \int_C \textbf{F} \cdot d\textbf{r} $, where $ \textbf{F}(x, y, z) = yze^x \, \textbf{i} + zxe^y \, \textbf{j} + xye^z \, \textbf{k}$ and $ \textbf{r}(t) = \sin t \, \textbf{i} + \cos t \, \textbf{j} + \tan t \, \textbf{k} $, $ 0 \leqslant t \leqslant \pi/4 $

Answer

$0.927136$

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