Q5. Consider the vector field F(x, y, z)=xi + 2yj + (x² + 4y²) k and the closed surface S made up of two pieces: the paraboloid z = 9 - (x² + y²), with z > 0, and its circular base x² + y² = 9, with z = 0. Use the divergence theorem to calculate the total flux of F across the surface S.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Q5. Consider the vector field
F(x, y, z) = xi + 2yj + (x² + 4y²)k
and the closed surface S made up of two pieces:
the paraboloid z = 9- (2²+ y²), with z>0, and
its circular base x² + y² = 9, with z = 0.
Use the divergence theorem to calculate the total flux of F across the surface S.
Transcribed Image Text:Q5. Consider the vector field F(x, y, z) = xi + 2yj + (x² + 4y²)k and the closed surface S made up of two pieces: the paraboloid z = 9- (2²+ y²), with z>0, and its circular base x² + y² = 9, with z = 0. Use the divergence theorem to calculate the total flux of F across the surface S.
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