Stokes' theorem states that [[ (V x F) - ds = f F. dr. Verify Stokes' theorem by calculating both sides of the equation for the vector field F = z²i+y²zj+zzk and the unit square given by 0≤x≤ 1, y = 0 and 0 ≤ z ≤ 1, i.e. dS= dzdzj.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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Stokes' theorem states that
[[ (V × F) - ds = f F - dr.
Verify Stokes' theorem by calculating both sides of the equation for the vector field
F = r²i+y²zj+xzk
and the unit square given by
0≤x≤ 1, y = 0 and 0≤ ≤ 1, i.e. ds = dzdzj.
Transcribed Image Text:Stokes' theorem states that [[ (V × F) - ds = f F - dr. Verify Stokes' theorem by calculating both sides of the equation for the vector field F = r²i+y²zj+xzk and the unit square given by 0≤x≤ 1, y = 0 and 0≤ ≤ 1, i.e. ds = dzdzj.
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