Use the Divergence Theorem to find the flux of F = xy 2 i + x 2
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Use the Divergence Theorem to find the flux of F = xy^{2}i + x^{2}yj + yk outward through the surface of the region enclosed by the cylinder x^{2} + y^{2} = 1 and the planes z = 1 and z = 1.
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THEOREM 8Divergence 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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Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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