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Evaluate the Line Integral Cxydx+(xy)dy\int _ { C } x y d x + ( x - y ) d y

Question 173

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Evaluate the line integral Cxydx+(xy)dy\int _ { C } x y d x + ( x - y ) d y , where C is the arc of the circle x2+y2=1x ^ { 2 } + y ^ { 2 } = 1 from the point (1,0)( 1,0 ) to the point (0,1)( 0,1 ) , followed by the line segment from the point (0,1)( 0,1 ) to the point (4,3)( 4,3 ) .

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