Question

Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = x\textsuperscript{2}i + 3xj + z\textsuperscript{2}k around the curve C: the ellipse 9x\textsuperscript{2} + y\textsuperscript{2} = 2 in the xy-plane, counterclockwise when viewed from above. $\oint_C \mathbf{F} \cdot d\mathbf{r} = 2\pi$ (Type an exact answer, using $\pi$ as needed.) 

          Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = x\textsuperscript{2}i + 3xj + z\textsuperscript{2}k around the
curve C: the ellipse 9x\textsuperscript{2} + y\textsuperscript{2} = 2 in the xy-plane, counterclockwise when viewed from above.
$\oint_C \mathbf{F} \cdot d\mathbf{r} = 2\pi$
(Type an exact answer, using $\pi$ as needed.)
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Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = x2i + 3xj + z2k around the curve C: the ellipse 9x2 + y2 = 2 in the xy-plane, counterclockwise when viewed from above. 𝐅· d𝐫 = 2π (Type an exact answer, using π as needed.)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Why is it 2π and not π? Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = xi + 3xj + zk around the curve C: the ellipse 9x^2 + y^2 = 2 in the xy-plane, counterclockwise when viewed from above. ∮F·dr = 2πT C (Type an exact answer, using t as needed.)
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Transcript

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00:01 So here in this question we are given the field f vector that is equal to x raised to the power 2 of i cap or i vector plus 4 of x j vector plus z raised to the power 2 of k vector so from here we are considering about the curl of f so curl of f from here is equal to derivation of i vector j vector and k vector this was from curly divided by the curly of x curly divided by the curly of y curly divided by the curly of z this is x raised to the power to 4 of x and z raised to the power 2 solving this it will become equals to i vector 0 minus 0 minus of j vector this is 0 minus 0 plus of k vector that is 4 minus 0 so solving this term so from here we can say that the curl of f will become equal to 4 of k dash now from here we are given the curve c on the ellipse that is x x x x to the power 2 divided by the 4…
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