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A vector $u=-2y\hat{i}+2x\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively. Evaluate the line integral

$$I=\oint _{C}u.dr$$

where $C$ is a closed loop formed by connecting points $(1,1),(3,1),(3,2)$ and $(1,2)$ in that order. The value of $I$ is ___________.
in Calculus recategorized by
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