Math Problem Statement
Verify Stoke's theorem for F=x i+z² j+ y² k where s is the plane x+y+z lying in first octant. Verify both LHS and RHS of Stoke's theorem
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Calculus
Stokes' Theorem
Surface Integrals
Line Integrals
Formulas
Stokes' Theorem: ∮_∂S F · dr = ∬_S (∇ × F) · dS
Curl of F: ∇ × F = (∂k/∂y - ∂j/∂z)i - (∂k/∂x - ∂i/∂z)j + (∂j/∂x - ∂i/∂y)k
Theorems
Stokes' Theorem
Suitable Grade Level
Undergraduate Level
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