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GATE EE 2020 Set 1 — Question 54

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NAT+2 / -0MediumLine, Surface & Volume IntegralsVector CalculusEngineering Mathematics

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

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Question

Let ax\mathbf{a}_x and ay\mathbf{a}_y be unit vectors along xx and yy directions, respectively. A vector function is given byF=axy−ayx\mathbf{F} = \mathbf{a}_x y - \mathbf{a}_y xThe line integral of the above function∫CF⋅dl\int_C \mathbf{F} \cdot d\mathbf{l}along the curve CC, which follows the parabola y=x2y = x^2 as shown below is ________ (rounded off to 2 decimal places).
Curve C on the parabola y = x squared, from the point x = -1, y = 1 down through the origin and up to the point x = 2, y = 4. Arrows show the direction of travel from x = -1 toward x = 2. Dashed lines mark x = -1, y = 1 and x = 2, y = 4.
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