- #1
Benny
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Hi, I posted a question some time ago and the suggestion was to use some form of the product rule but I still can't figure out what to do.
Q. Let f(x,y,z) and g(x,y,z) be C^2 scalar functions. Let D be an elementary region in space and [tex]\partial D[/tex] be the closed surface that bounds D. Prove that
[tex]\int\limits_{}^{} {\int\limits_{}^{} {\int\limits_D^{} {\nabla f \bullet \nabla g} dV = \int\limits_{}^{} {\int\limits_{\partial D}^{} {f\nabla g \bullet dS} - \int\limits_{}^{} {\int\limits_{}^{} {\int\limits_D^{} {f\nabla ^2 gdV} } } } } } [/tex]
Can someone give me a hint as to where to start, like any relevant identies which could be of use? Any help is appreciated thanks.
Q. Let f(x,y,z) and g(x,y,z) be C^2 scalar functions. Let D be an elementary region in space and [tex]\partial D[/tex] be the closed surface that bounds D. Prove that
[tex]\int\limits_{}^{} {\int\limits_{}^{} {\int\limits_D^{} {\nabla f \bullet \nabla g} dV = \int\limits_{}^{} {\int\limits_{\partial D}^{} {f\nabla g \bullet dS} - \int\limits_{}^{} {\int\limits_{}^{} {\int\limits_D^{} {f\nabla ^2 gdV} } } } } } [/tex]
Can someone give me a hint as to where to start, like any relevant identies which could be of use? Any help is appreciated thanks.