Find this integral ∫∫ curl (x²y i - xz k) . n dσ over the closed surface of the ellipsoid x²/4 + y²/9 + z²/16?
Find this integral ∫∫ curl (x²y i - xz k) . n dσ over the closed surface of the ellipsoid x²/4 + y²/9 + z²/16 = 1.
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Apply the Divergence Theorem.
∫∫s curl (x²y i - xz k) · n dσ
= ∫∫∫ div (curl (x²y i - xz k)) dV, since the surface is closed
= 0, since div(curl F) = 0.
I hope this helps!