[Solution] Calculate \oint F • n#770; d s with the field F(x, y)=[c2 x-3 y^2 , x^3+5 y], over the elliptic path γ parametrized by
Question: Calculate \(\oint \vec{F} \cdot \hat{n} d s\) with the field \(\vec{F}(x, y)=\left[\begin{array}{c}2 x-3 y^{2} \\ x^{3}+5 y\end{array}\right]\), over the elliptic path \(\gamma\) parametrized by
\[\vec{r}(t)=\left[\begin{array}{l} 3 \cos t \\ 2 \sin t \end{array}\right], \text { for } \pi \leq t \leq 3 \pi\]
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Solution: Find the area of that portion of the paraboloid x=9-y^2-z^2
![[Solution Library] Find the flux of the](/images/solutions/MC-solution-library-46350.jpg "[Solution Library] Find the flux of the field F(x, y, z)=< 1,-3 z^2, 3")
[Solution Library] Find the flux of the field F(x, y, z)=< 1,-3 z^2, 3
(See) Compute the (outward) flux of the field F(x, y, z)=[c10
![[Solved] Let F(x, y, z)=[c9 x+2 z](/images/solutions/MC-solution-library-46352.jpg "[Solved] Let F(x, y, z)=[c9 x+2 z , y-3 x , x^2 tan ^-1(y z)],")
[Solved] Let F(x, y, z)=[c9 x+2 z , y-3 x , x^2 tan ^-1(y z)],
![[See Solution] Let F(x, y, z)=[cy e^2](/images/solutions/MC-solution-library-46353.jpg "[See Solution] Let F(x, y, z)=[cy e^2 z , x e^2 z , 2 x y e^2")
[See Solution] Let F(x, y, z)=[cy e^2 z , x e^2 z , 2 x y e^2
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