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Use Stoke's Theorem to Evaluate CC Is the Curve of Intersection of the Hyperbolic Paraboloid

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Short Answer

Use Stoke's theorem to evaluate CFdr,F(x,y,z)=6yx2i+2x3j+6xyk\int _ { C } \mathbf { F } \cdot d \mathbf { r } , \mathbf { F } ( x , y , z ) = 6 y x ^ { 2 } \mathbf { i } + 2 x ^ { 3 } \mathbf { j } + 6 x y \mathbf { k } ,
CC is the curve of intersection of the hyperbolic paraboloid z=y2x2z = y ^ { 2 } - x ^ { 2 } and the cylinder x2+y2=25x ^ { 2 } + y ^ { 2 } = 25 oriented counterclockwise as viewed from above.


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