Problem #8: Use Stokes' Theorem to evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F} = (x + 8z)\mathbf{i} + (7x + y)\mathbf{j} + (2y - z)\mathbf{k}$ and $C$ is the curve of intersection of the plane $x + 4y + z = 24$ with the coordinate planes. (Assume that $C$ is oriented counterclockwise as viewed from above.) Problem #8: 1391.6 Just Save Your work has been saved! (Back to Admin Page) Submit Problem #8 for Grading Problem #8 Your Answer: Your Mark: Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 1391.6 0/2x
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Step 1: Stokes' Theorem states that $\int_C \textbf{F} \cdot d\textbf{r} = \iint_S (\nabla \times \textbf{F}) \cdot \textbf{n} dS$, where S is any surface with C as its boundary, and $\textbf{n}$ is the unit normal vector to S. Show more…
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Use Stokes' Theorem to evaluate ∧_C F ∙ dr where F = (x + 6z) i + (8x + y) j + (5y − z) k and C is the curve of intersection of the plane x + 4y + z = 16 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.)
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$7-10$ Use Stokes' Theorem to evaluate $\int_{C} \mathbf{F} \cdot d \mathbf{r} .$ In each case $C$ is oriented counterclockwise as viewed from above. $$\begin{array}{l}{\mathbf{F}(x, y, z)=x y \mathbf{i}+2 z \mathbf{j}+3 y \mathbf{k}, \quad C \text { is the curve of intersec- }} \\ {\text { tion of the plane } x+z=5 \text { and the cylinder } x^{2}+y^{2}=9}\end{array}$$
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