Index Notation Help: Solving ∫∂k(gixiεjklxl)dV

[squire636]

Homework Statement

∫ ∂_k(g_ix_iε_jklx_l dV

Can anyone make sense of this? I know I'll need to apply the chain rule when taking the derivative, but I'm not quite sure how to proceed. Also, this is part of a larger problem where g is a gravity vector existing purely in the -z direction, but I treated this as a constant and pulled it outside the integral and got:

g ∫ ∂_k(x_iε_jklx_l) dV

Homework Equations

The Attempt at a Solution

I don't think we need to get rid of the integral at all, and I'm pretty sure that the final solution will have something of the form: ∫ x x ( ) dV (that is a cross product). The TA for the course said that we should get to this, and we need to figure out what is inside the parentheses.

Thanks!

 

[Muphrid]

There's no chain rule here; just the product rule. What's $\partial_k x_i$?

 

[voko]

If this is tensor notation, then it is simply wrong, because repeated indices there occur all at the bottom. You will have to use LaTeX to make your problem understandable. Speaking of which, knowing what the problem is about would be useful.