The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y, (1 — z)²). Calculate the divergence of the vector field A(r). Hence evaluate the integral JJJ where W is the volume enclosed by the (x, y)-plane and the surface H. The volume element dV for your chosen coordinate system may be quoted without derivation if you wish. V.A dV,

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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3. The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given
by A = (x, y, (1 — z)²).
Calculate the divergence of the vector field A(r). Hence evaluate the integral
JJJw
V.AdV,
where W is the volume enclosed by the (x, y)-plane and the surface H. The volume
element dV for your chosen coordinate system may be quoted without derivation
if you wish.
Transcribed Image Text:3. The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y, (1 — z)²). Calculate the divergence of the vector field A(r). Hence evaluate the integral JJJw V.AdV, where W is the volume enclosed by the (x, y)-plane and the surface H. The volume element dV for your chosen coordinate system may be quoted without derivation if you wish.
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