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Using Either Stokes' Theorem or the Divergence Theorem (Whichever Is Q˙((2x+cosyz)i+(5y+sin2z)j+(3z+x)k)×dA\dot{\mathrm{Q}}((2 x+\cos y z) \vec{i}+(5 y+\sin 2 z) \vec{j}+(3 z+x) \vec{k}) \times d \vec{A}

Question 66

Essay

Using either Stokes' theorem or the Divergence theorem (whichever is appropriate), evaluate Q˙((2x+cosyz)i+(5y+sin2z)j+(3z+x)k)×dA\dot{\mathrm{Q}}((2 x+\cos y z) \vec{i}+(5 y+\sin 2 z) \vec{j}+(3 z+x) \vec{k}) \times d \vec{A} where S is the sphere of radius 2 oriented outward and centered at the point (2,e25,π2)\left( 2 , e ^ { - 25 } , \pi ^ { 2 } \right)

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