$Stokes' theorem $\int_S \nabla \times F \cdot dS= \int_C F\cdot dr$ verification$

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$Stokes' theorem $\int_S \nabla \times F \cdot dS= \int_C F\cdot dr$ verification$

Verify Stokes' theorem
$$\int_S \nabla \times F \cdot dS= \int_C F\cdot dr$$
where $F=(2x,3xy^2,5z)$ where $S$ is the surfce of the paraboloid
\[z=4-x^2-y^2, z\geq 0\]
and $C=\partial S$.

Multivariable Calculus Stokes' Theorem Integrals

Bill Space

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$Stokes' theorem $\int_S \nabla \times F \cdot dS= \int_C F\cdot dr$ verification$

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