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Mathematics, 27.05.2020 18:57 kcombest7219

Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector field, surface S, and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation. Fequals=left angle negative y comma negative x minus z comma y minus x right angle−y,−x−z, y−x; S is the part of the plane zequals=55minus−y that lies in the cylinder xsquared2plus+ysquared2equals=44 and C is the boundary of S. Construct the line integral of Stokes' Theorem using the parameterization r(t)equals=left angle 2 cosine t comma 2 sine t comma 5 minus 2 sine t right angle2cost,2sint,5−2sint, 0less than or equals≤tless than or equals≤2piπ, for C. Choose the correct answer below

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