Partial integration in full integration

Hello all,

I am trying to calculate the induced voltage in a coil in the time domain, the formula is:

V=int(part(A)/part(t)dl)

i hope you get the idea, that is a line integral for one filament of a coil, dl being part of the length of the wire. i need to integrate the partial magnetic vector potential (A) for each time step along the wire.