Verify Stokes Theorem for the vector field F = 2xyi + xj + ( y + z)k
Question:
Verify Stokes’ Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x2 - y2, z ≥ 0, oriented with unit normal n pointing upward.
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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: fF.dr = [[ S Counterclockwise circulation VXF ndo Curl integral (4)
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To apply Stokes Theorem we need to find the curl of the vector field F and the boundary curve of the surface First lets find the curl of F curl F Qy P...View the full answer
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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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