(See Solution) Suppose (partial N)/(∂ x)-(partial M)/(∂ y)=(3-x)^2 y within the region R enclosed by the right triangle in Quadrant I enclosed by
Question: Suppose \(\frac{\partial N}{\partial x}-\frac{\partial M}{\partial y}=(3-x)^{2} y\) within the region \(R\) enclosed by the right triangle in Quadrant \(I\) enclosed by the coordinate axes and the line \(x+y=3\). Then \(\oint M d x+N d y=\) ?
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![[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
(See) Compute the (outward) flux of the field F(x, y, z)=[c10
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