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Let be f and g scalar functions on $\mathbb{R}^3$ and $f_{{x}_i}$ denotes partial differentiation of f with respect to the i-th Cartesian coordinate, when this equality is true:

$$\int_{S^2(R)} f_{x_{i}}g(x)dx=-\int_{S^2(R)} f(x)g_{x_{i}}dx$$

where $S^2(R)$ is the sphere of radius $R$ centered at origin.

What conditions does it true for f and g??

Hugus
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    Is this a volume integral, a surface integral, or a line integral? dx only makes sense for a line integral, but then in what way are you integrating over the sphere? – Aaron Lockey Nov 09 '13 at 06:47
  • I think this is a surface Integral... notation is unusual – Hugus Nov 09 '13 at 13:34

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