Let S be the cylinder x 2 + y 2 = a 2 , 0 z
Question:
Let S be the cylinder x2 + y2 = a2, 0 ≤ z ≤ h, together with its top, x2 + y2 ≤ a2, z = h. Let F = -yi + xj + x2k. Use Stokes’ Theorem to find the flux of ∇ * F outward through S.
Transcribed Image Text:
THEOREM 6-Stokes' Theorem Let S be a piecewise smooth oriented surface having a piecewise smooth boundary curve C. Let F = Mi + Nj + Pk be a vector field whose components have continuous first partial derivatives on an open region containing S. Then the circulation of F around C in the direction counterclockwise with respect to the surface's unit normal vector n equals the integral of the curl vector field VX F over S: & F ·dr = [[ F.dr S Counterclockwise circulation VXF n do Curl integral (4)
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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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