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Evaluate the outward flux ∫∫S(F·n)dS of the vector fieldF=yz(x^2+y^2)i−xz(x^2+y^2)j+z^2(x^2+y^2)k, where S is the surface of the...

Evaluate the outward flux ∫∫S(F·n)dS of the vector fieldF=yz(x^2+y^2)i−xz(x^2+y^2)j+z^2(x^2+y^2)k, where S is the surface of the region bounded by the hyperboloid x^2+y^2−z^2= 1, and the planes z=−1 and z= 2.

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