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Use Stokes's Theorem to Evaluate F(x,y,z)=xyzi+yj+zk,x2+y249\mathbf { F } ( x , y , z ) = x y z \mathbf { i } + y \mathbf { j } + z \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 49

question 64

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Use Stokes's Theorem to evaluate F(x,y,z) =xyzi+yj+zk,x2+y249\mathbf { F } ( x , y , z ) = x y z \mathbf { i } + y \mathbf { j } + z \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 49 and SS is the first-octant portion of z=x2z = x ^ { 2 } over x2+y2=49x ^ { 2 } + y ^ { 2 } = 49
Use a computer algebra system to verify your result.


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