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Question 6 of 9 < > If curl $\vec{F} = (x^2 + z^2)\vec{j} + 7\vec{k}$, find $\int_C \vec{F} \cdot d\vec{r}$, where C is a circle of radius 7, centered at the origin, with the following conditions: NOTE: Enter exact answers, or round to three decimal places. (a) C in the xy-plane, oriented counterclockwise when viewed from above. $\int_C \vec{F} \cdot d\vec{r} = $ (b) C in the xz-plane, oriented counterclockwise when viewed from the positive y-axis. $\int_C \vec{F} \cdot d\vec{r} = $

          Question 6 of 9
< >
If curl $\vec{F} = (x^2 + z^2)\vec{j} + 7\vec{k}$, find $\int_C \vec{F} \cdot d\vec{r}$, where C is a circle of radius 7, centered at the origin, with the following conditions:
NOTE: Enter exact answers, or round to three decimal places.

(a) C in the xy-plane, oriented counterclockwise when viewed from above.

$\int_C \vec{F} \cdot d\vec{r} = $

(b) C in the xz-plane, oriented counterclockwise when viewed from the positive y-axis.

$\int_C \vec{F} \cdot d\vec{r} = $

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question 6 of 9 if curl vecf x2 z2vecj 7veck find intc vecf cdot dvecr where c is a circle of radius 7 centered at the origin with the following conditions note enter exact answers or round 48273

Added by Tiffany O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

11/29/2023

Step 1

According to Stokes' Theorem, $\int_C \vec{F} \cdot d\vec{r} = \iint_S (\text{curl } \vec{F}) \cdot d\vec{S}$, where S is any surface with boundary C. In this case, C is a circle of radius 7 centered at the origin. We can choose S to be the disk bounded by C. The Show more…

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Question 6 of 9 < > If curl $\vec{F} = (x^2 + z^2)\vec{j} + 7\vec{k}$, find $\int_C \vec{F} \cdot d\vec{r}$, where C is a circle of radius 7, centered at the origin, with the following conditions: NOTE: Enter exact answers, or round to three decimal places. (a) C in the xy-plane, oriented counterclockwise when viewed from above. $\int_C \vec{F} \cdot d\vec{r} = $ (b) C in the xz-plane, oriented counterclockwise when viewed from the positive y-axis. $\int_C \vec{F} \cdot d\vec{r} = $

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