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Evaluate the Line Integral ∫CF⋅dr\int _ { C } \mathbf { F } \cdot d \mathbf { r }

Question 172

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Evaluate the line integral ∫CF⋅dr\int _ { C } \mathbf { F } \cdot d \mathbf { r } , where F(x,y)=exi+xyj\mathbf { F } ( x , y ) = e ^ { x } \mathbf { i } + x y \mathbf { j } and the curve CC is given by the vector function r(t)=t2i+t3j,0≤t≤1\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 0 \leq t \leq 1 .

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