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Find, by direct computation, the line integral of yi⃗−xj⃗y \vec { i } - x \vec { j }yi−xj around the circle r⃗(t)=costi⃗+sintj⃗,0≤t≤2π\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { j } , 0 \leq t \leq 2 \pir(t)=costi+sintj,0≤t≤2π
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