Verify that Stokes Theorem is true for the vector field F = 7yzi-yj + 2xk and...

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Verify that Stokes Theorem is true for the vector field F = 7yzi-yj + 2xk and the surface S the part of the paraboloid z = 7 - x² - y² that lies above the plane z = 3, oriented upwards. ute la To verify Stokes' Theorem we will compute the expression on each side. First compute curl F== where curl curl F. dS= n -[f curl F curl F. dS= Now compute of F C F. dr = F. dr. II. X1 x₂ == Σ M. M Σ The boundary curve C of the surface S can be parametrized by: r(t) = ). 05152x Σ E dr Σ dydx y₁ = 3/2 == =(2 cos(t). (Use the most natural parametrization) curl F. dS Σ MM Σ Verify that Stokes Theorem is true for the vector field F = 7yzi-yj + 2xk and the surface S the part of the paraboloid z = 7 - x² - y² that lies above the plane z = 3, oriented upwards. ute la To verify Stokes' Theorem we will compute the expression on each side. First compute curl F== where curl curl F. dS= n -[f curl F curl F. dS= Now compute of F C F. dr = F. dr. II. X1 x₂ == Σ M. M Σ The boundary curve C of the surface S can be parametrized by: r(t) = ). 05152x Σ E dr Σ dydx y₁ = 3/2 == =(2 cos(t). (Use the most natural parametrization) curl F. dS Σ MM Σ

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