Find the flux of F = (3z + 1)k upward across the hemisphere x 2 + y
Question:
Find the flux of F = (3z + 1)k upward across the hemisphere x2 + y2 + z2 = a2, z ≥ 0
(a) With the Divergence Theorem and
(b) By evaluating the flux integral directly.
Transcribed Image Text:
THEOREM 8-Divergence Theorem Let F be a vector field whose compo- nents have continuous first partial derivatives, and let S be a piecewise smooth oriented closed surface. The flux of F across S in the direction of the surface's outward unit normal field n equals the triple integral of the divergence V. F over the region D enclosed by the surface: [₁ F.ndo = Outward flux J V.F dV. Divergence integral (2)
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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