Question

Use Stoke's Theorem to evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x, y, z) = z\mathbf{i} + y\mathbf{j} + 9(x^2 + y^2)\mathbf{k}$ and $C$ is the boundary of the part of the paraboloid where $z = 64 - x^2 - y^2$ which lies above the xy-plane and $C$ is oriented counterclockwise when viewed from above.\ $\text{curl } \mathbf{F} = \begin{pmatrix} 18y & 18x & 0 \end{pmatrix}$ line integral =

          Use Stoke's Theorem to evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x, y, z) = z\mathbf{i} + y\mathbf{j} + 9(x^2 + y^2)\mathbf{k}$ and $C$ is the boundary of the part of the paraboloid where $z = 64 - x^2 - y^2$ which lies above the xy-plane and $C$ is oriented counterclockwise when viewed from above.\
$\text{curl } \mathbf{F} = \begin{pmatrix} 18y & 18x & 0 \end{pmatrix}$ 
line integral =

Use Stoke's Theorem to evaluate 𝐅· d𝐫 where 𝐅(x, y, z) = z𝐢 + y𝐣 + 9(x^2 + y^2)𝐤 and C is the boundary of the part of the paraboloid where z = 64 - x^2 - y^2 which lies above the xy-plane and C is oriented counterclockwise when viewed from above.curl 𝐅 =
< p m a t r i x >
line integral =

Added by Eric L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

01/06/2023

Step 1

Step 1: Calculate the curl of F: The curl of F is given by curlF = <18x, 18y, 0>. Show more…

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Use Stoke's Theorem to evaluate int_C F*dr where F(x,y,z)=xi +yj+9(x^(2)+y^(2))k and C is the boundary of the part of the para where z=64-x^(2)-y^(2) which lies above the xy-plane and C is oriented counterclockwise when viewed from above. curlF=(:1,18x,0:) line integral = Use Stoke's Theorem to evaluate F . dr where F(,y,z)=i +yj+(2+y2k and C is the boundary of the part of the para where z = 64 -- 2 -- y2 which lies above the xy-plane and C is oriented counterclockwise when viewed from above. curlF= 18y 18x line integral =