Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise The circulation line integral of F = (3xy2,5x³ + y) where C is the boundary of {(x,y): 0≤y≤ sinx, 0≤x≤)} fF.dr = C Tyne an exact answer, using it as needed) Scanner ...

Q: Evaluate the line integral y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

A: Consider the provided question,

Q: 3 Let S be a square plate with boundary C having length of each side as 2 units and lying in the…

A: The plane is given as y = 1, so plane S is y = 1   The unit normal vector to the surface S is:

Q: Calculate the line integral F•r'ds by Stokes's theorem, clockwise as seen by a person standing at…

A: Before applying the Stokes theorem we have to find the normal vector to the plane that has the…

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. O x2y dx,…

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Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $c…

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Q: Consider the curve C = C1 ∪ C2 ∪ C3 ∪ C4, piecewise smooth, oriented from the point A(1, 1, 2) to…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. S (4…

A: The given line integral is ,              ∫c  4e5y dx+ 3 e5x dy where c is the rectangle with…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-4*…

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Q: Let → F = . Use Stokes' Theorem to evaluate SSS curl → F.d S, where S is the hemisphere x^2 + y^2 +…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 2…

A: Evaluate: ∮C2y2dx+2x2dy where C is the square with the vertices 0,0, 3,0, 3,3, 0,3 oriented…

Q: Consider the contour represented in the following figure. The points marked on the figure are А(3,…

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