Huh? You don't consider numerical methods that approximate integrals to be true calculus?

This is true calculus. You don't need to know anything about the future voltage curve or current, just the past.

This is the equation to calculate capacity consumed in a battery (which is a numerical approximation to an integral):

capacity consumed = capacity at last check + (current + current at last check)/2*(present time - time at last check)

The equation above is the trapezoidal rule (http://en.wikipedia.org/wiki/Trapezoidal_rule) applied to the integral in my first post.

I hate to pull this one out, but trust me, I'm a battery scientist that makes mathematical models of batteries for a living.