Integrating Electric Displacement

[kNYsJakE]

Suppose the dielectric material is fixed in position and filling the capacitor, and you would have this term in the way of calculating something.

\int\nabla\cdot\left[\left(\Delta{D}\right){V}\right]{d}\tau

where D is the dielectric displacement

Now that turns into (by divergence theorem):

\int\left(\nabla{D}{V}\right)\cdot{d}a

Now my textbook says that this term would vanish if we integrate over all of space. Why is that? Thanks for your help in advance. =)

 

[kNYsJakE]

By the way, this is from pg 192 of Electrodynamics by Griffiths, if this could help..