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GATE EC 2021 Set 1 — Question 11

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MCQ+1 / -0.33MediumLine, Surface & Volume IntegralsVector CalculusEngineering Mathematics

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

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Question

The vector function F(r)=−xi^+yj^\mathbf{F}(\mathbf{r}) = -x\hat{i} + y\hat{j} is defined over a circular arc CC shown in the figure.
A circular arc C in the first quadrant of a coordinate system. The arc starts at (1,0) on the x-axis and ends at a point on the unit circle that makes a 45-degree angle with the positive x-axis. Unit vectors i-hat and j-hat are shown along the x and y axes respectively.
The line integral of ∫CF(r)⋅dr\int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r} is
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