I think I wasn't quite clear in what I meant. d is the distance that your center of mass changes while your feet are in contact with the ground (While you are doing work) and h is the height that your center of mass changes while you are in the air.

Saying a force is impulsive means that you making certain assumptions to make your calculation easier. It doesn't change the fact that W = integral of force dotted with displacement. It is true that I am making a big approximation where I say that the force is constant over the jump, making the integral evaluate to f * x.

Thanks for the link. I think this kind of stuff is very interesting.