- #1
WWCY
- 479
- 12
Homework Statement
Could someone illustrate why
$$\int_{V} \nabla \cdot (f\vec{A}) \ dv = \int_{V} f( \nabla \cdot \vec{A} ) \ dv + \int_{V} \vec{A} \cdot (\nabla f ) \ dv = \oint f\vec{A} \cdot \ d\vec{a}$$
?
Homework Equations
The Attempt at a Solution
I understand that the integrand can be split by using vector product rules to give two integrals, but I don't see how the divergence theorem,
$$\int_{V} (\nabla \cdot \vec{A}) \ dv = \oint \vec{A} \cdot d\vec{a}$$
gets me from step 2 to 3.
Assistance is greatly appreciated!