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GATE ME 2016 Set 3 — Question 37

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NAT+2 / -0MediumLine, Surface & Volume IntegralsVector CalculusEngineering MathematicsGreen's Theorem

Engineering Mathematics → Vector Calculus → Green's Theorem

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Question

The value of the line integral ∮CF⃗⋅r⃗′ds\oint_C \vec{F} \cdot \vec{r}' ds, where CC is a circle of radius 4π\frac{4}{\sqrt{\pi}} units is ________
Here, F⃗(x,y)=yi^+2xj^\vec{F}(x, y) = y \hat{i} + 2x \hat{j} and r⃗′\vec{r}' is the UNIT tangent vector on the curve CC at an arc length ss from a reference point on the curve. i^\hat{i} and j^\hat{j} are the basis vectors in the x−yx-y Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
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