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GATE EC 2019 Set 1 — Question 37

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MCQ+2 / -0.67MediumGauss, Stokes & Green's TheoremsVector CalculusEngineering Mathematics

Engineering Mathematics → Vector Calculus → Gauss, Stokes & Green's Theorems

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Question

Consider the line integral∫C(xdy−ydx)\int_C (x dy - y dx)the integral being taken in a counterclockwise direction over the closed curve CC that forms the boundary of the region RR shown in the figure below. The region RR is the area enclosed by the union of a 2×32 \times 3 rectangle and a semi-circle of radius 11. The line integral evaluates to
Region R consisting of a rectangle and a semi-circle
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