Miscellaneous integral identities Prove the following

QUESTION:

Miscellaneous integral identities Prove the following identities.

a. \(\iiint_{D} \nabla \times \mathbf{F} d V=\iint_{S}(\mathbf{n} \times \mathbf{F}) d S\) (Hint: Apply me Divergence Theorem to each component of the identity.)

b. \(\iint_{S}(\mathbf{n} \times \nabla \varphi) d S=\oint_{C} \varphi d \mathbf{r}\)Hin1: Apply Stokes' Theorem lo each component of the identity.)

Text Transcription:

iiint_D nabla x F dV = iint_S (n x F) dS

iint_S (n x nabla_varphi) dS = oint_c varphi dr