[Solution] Calculate the area of the region bounded by the simple closed curve γ parametrized for 0 ≤q t ≤q 2 by
Question: Calculate the area of the region bounded by the simple closed curve \(\gamma\) parametrized for \(0 \leq t \leq 2\) by
\[\vec{r}(t)=\left[\begin{array}{c} 2 \cos (\pi t)-\sin (\pi t) \\ 5 \sin (\pi t)-3 \cos (\pi t) \end{array}\right]\]
Deliverable: Word Document 
(Steps Shown) Suppose (partial N)/(∂ x)-(partial M)/(∂
![[Steps Shown] Calculate vecF • d r](/images/solutions/MC-solution-library-46347.jpg "[Steps Shown] Calculate vecF • d r with the field F from problem")
[Steps Shown] Calculate vecF • d r with the field F from problem
![[All Steps] Calculate \oint F • n#770;](/images/solutions/MC-solution-library-46348.jpg "[All Steps] Calculate \oint F • n#770; d s with the field")
[All Steps] Calculate \oint F • n#770; d s with the field
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
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