What is the term for resistance to change in current and what is its correct formula?
they always base the equation off the assumption that the voltage is
  continuously changing. The equation is X(L) = 2piFL


That's actually not quite right.  The correct assumption is that the voltage is sinusoidal.  There are an infinity of voltage waveforms that are continuously changing but are not sinusoidal.

More generally, for an ideal inductor, the voltage across the inductor is proportional the time rate of change of the current through the inductor.  If you place a constant voltage across an inductor, the current changes at a constant rate.

So, generally, the voltage across an inductor does not have the same form as the current through the inductor; the waveforms "look" different.

However, if the current is a sine wave, the voltage will be a sine wave though there will be a difference in phase.

Since both the current and voltage have the same form, we can take the ratio of the magnitudes of the voltage and current sine waves and call that ratio the reactance.  Since higher frequency sine waves change more rapidly, the reactance increases with frequency.

For analyzing non-sinusoidal waveforms, like a square wave, one can use calculus to find the average current in the time domain.  If your voltage source and inductor are ideal, the current waveform for a voltage square wave would be triangle wave:



not a parabolic wave.  If there is significant internal resistance, the current looks more like:



So, your parabolic current waveform isn't the result of applying a voltage square wave across an inductor.