Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the square surface y 2, oriented positively, with vertices %3D (0,2,0), (0,2,2), and (2,2,2), and (2,2,0).

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Q: the surface z = &x + 4y th=

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Q: Calculate the surface area of the z=x²+y surface on the triangular region with vertices (0,0), (1,0)…

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

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A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

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Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

A: The given equation of the surface is x2 + 2y2 + z2 - 4x + 4y - 2z + 3 = 0.The general equation,…

Q: Find the points where line x-1-y+2=² intersects xy, yz and -1 1 2

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