Calculate the flux integral F.Nds, where the vector field F is given by F(x,y,z) = xzi +yzj + 2xk, where S is the upper hemisphere defined by x² + y² + z² = 4,z ≥ 0, and the unit normal Ñ has a positive k-component.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Calculate the flux integral
# F. Ñ dS,
XPS
where the vector field F is given by F(x,y,z) = xzi + yzj + 2xk, where S is the upper hemisphere
defined by x² + y² + z² = 4,z ≥ 0, and the unit normal Ñ has a positive k-component.
Transcribed Image Text:Calculate the flux integral # F. Ñ dS, XPS where the vector field F is given by F(x,y,z) = xzi + yzj + 2xk, where S is the upper hemisphere defined by x² + y² + z² = 4,z ≥ 0, and the unit normal Ñ has a positive k-component.
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