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Evaluate CFdr\int _ { C } \mathbf { F } d \mathbf { r }

question 9

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Evaluate CFdr\int _ { C } \mathbf { F } d \mathbf { r } where F(x,y) =(arctany,xy21+y2) \mathrm { F } ( x , y ) = \left( \arctan y , - \frac { x y ^ { 2 } } { 1 + y ^ { 2 } } \right) and the curve C is a triangle from (0,0) ( 0,0 ) , to (2,2) ( 2,2 ) , to (1,4) ( 1,4 ) , then back to (0,0) ( 0,0 ) .

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