What is the difference between ∫X.dY and ∫Y.dX in the physical world? I know what the difference is in pure mathematics. ∫X.dY represents the are bounded by the curve and the Y axis while ∫Y.dX represents the area bounded by the curve and the X axis. But I am unable to translate this into physical situations. For example when we are doing ∫F.dX, we are calculating force multiplied by displacement for very small displacements and then adding them all up. Similarly ∫X.dF should mean that we are multiplying the displacement of the particle for a very small change in F with that small change. Should they not mean the same thing and give the same result? Yet only the first is called the work done. One other example that I can think of is that of pressure-volume work. ∫p.dv is the work done. I can't even think of what ∫v.dp means. What does it mean?