Question

4.(10 points) (DO NOT INTEGRATE) Using Stokes' Theorem with an appropriate choice of Upper $S$, rewrite the given line integral $\oint_C \mathbf{F} d\mathbf{r}$ as an area integral over the appropriate region of the $xy$-plane. Assume that Upper $C$ has a counterclockwise orientation when viewed from above. $\mathbf{F} = (5y, -2z, x)$ $C$ is the circle $x^2 + y^2 = 7$ in the plane $z = 0$. $\oint_C \mathbf{F} d\mathbf{r} = \iint_S$ _________ $dS$

Name: 410 points do not integrate using stokes theorem with an appropriate choice of upper s rewrite the given line integral ointc mathbff dmathbfr as an area integral over the appropriate region 95535
Uploaded: 2023-01-09T04:54:07-08:00
Duration: 4 min 32 s
Channel: Sri K
Description: 410 points do not integrate using stokes theorem with an appropriate choice of upper s rewrite the given line integral ointc mathbff dmathbfr as an area integral over the appropriate region 95535

          4.(10 points) (DO NOT INTEGRATE) Using Stokes' Theorem with an appropriate choice of Upper $S$, rewrite the given line integral $\oint_C \mathbf{F} d\mathbf{r}$ as an area integral over the appropriate region of the $xy$-plane. Assume that Upper $C$ has a counterclockwise orientation when viewed from above.
$\mathbf{F} = (5y, -2z, x)$
$C$ is the circle $x^2 + y^2 = 7$ in the plane $z = 0$.
$\oint_C \mathbf{F} d\mathbf{r} = \iint_S$ _________ $dS$

410 points do not integrate using stokes theorem with an appropriate choice of upper s rewrite the given line integral ointc mathbff dmathbfr as an area integral over the appropriate region 95535

Added by Gerald D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/09/2023

Step 1

Stokes' Theorem states that $\oint_C \mathbf{F} d\mathbf{r} = \iint_S (\nabla \times \mathbf{F}) \cdot d\mathbf{S}$, where $S$ is any surface whose boundary is $C$. Show more…

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4.(10 points) (DO NOT INTEGRATE) Using Stokes' Theorem with an appropriate choice of Upper $S$, rewrite the given line integral $\oint_C \mathbf{F} d\mathbf{r}$ as an area integral over the appropriate region of the $xy$-plane. Assume that Upper $C$ has a counterclockwise orientation when viewed from above. $\mathbf{F} = (5y, -2z, x)$ $C$ is the circle $x^2 + y^2 = 7$ in the plane $z = 0$. $\oint_C \mathbf{F} d\mathbf{r} = \iint_S$ _________ $dS$