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GATE EE 2023 Set 1 — Question 62

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NAT+2 / -0MediumLine, Surface & Volume IntegralsVector CalculusEngineering MathematicsStokes, Gauss & Green's Theorems

Engineering Mathematics → Vector Calculus → Line, Surface & Volume Integrals

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Question

The closed curve shown in the figure is described byr=1+cos⁡θr = 1 + \cos\theta, where r=x2+y2r = \sqrt{x^2 + y^2}; x=rcos⁡θ,y=rsin⁡θx = r\cos\theta, y = r\sin\thetaThe magnitude of the line integral of the vector field F=−yi^+xj^F = -y\hat{i} + x\hat{j} around the closed curve is ____________ (Round off to 2 decimal places).
A plot of the cardioid curve $r = 1 + \cos\theta$ in the $x$-$y$ plane
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