Think of temperature, which is a function of four variables (time, space, space and space). What does it mean to say "the derivative of temperature," if it's genuinely a function of all four things? What does it mean to say "the integral of temperature?" You'll find out!

Stokes' Theorem, Green's theorem, and the like are absolutely essential for much of our modern physics, which needs Calculus to study change, and multiple dimensions to study our big big world. Stokes' theorem, in a nutshell, says: The fluid flow around the outside of a coffee cup is equal to the total vorticity within the cup. (Or perhaps I've paraphrased it beyond repairWhat is ) The Divergence theorem, in a nutshell, says: The fluid flow out of the top of a (full) coffee cup is the flow into the cup plus total fluid expansion within the interior. Note: Rates of change + multiple dimensions = Calc III.

Many of the examples of Calculus 1 and 2 were artificial because the objects studied had to move in a line and change only in one dimension. With calculus 3, you can honestly study a satellite hurtling through space, affected by the gravities of many objects, and explain the nearby dustclouds as density functions. All this can be done with derivatives and integrals for added understanding.