Miscellaneous integral identities Prove the following identities.a. ∫∫∫D ∇ x F dV = ∫∫S (n x F) dS (Hint: Apply the Divergence Theorem to each component of the identity.)b. ∫∫S (n x ∇φ) dS = ∮C φ dr (Hint: Apply Stokes’ Theorem to each component of the identity.)

Miscellaneous integral identities Prove the following identities.a. ∫∫∫D ∇ x F dV = ∫∫S (n x F) dS (Hint: Apply the Divergence Theorem to each component of the identity.)b. ∫∫S (n x ∇φ) dS = ∮C φ dr (Hint: Apply Stokes’ Theorem to each component of the identity.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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Question

Miscellaneous integral identities Prove the following identities.
a. ∫∫∫_D ∇ x F dV = ∫∫_S (n x F) dS (Hint: Apply the Divergence Theorem to each component of the identity.)
b. ∫∫_S (n x ∇φ) dS = ∮_C φ dr (Hint: Apply Stokes’ Theorem to each component of the identity.)

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