∫ ∂k(gixiεjklxl 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(xiεjklxl) dV
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.