why does multivariable integration not work?

Question

d(PV)=VdP+PdV
Int(dPV)=int(VdP+PdV) != Int(VdP)+ int(PdV)

Why can you not distribute the integral?

In: 0

Answer 1

What does int(VdP+PdV) mean if not int(VdP) + int(PdV)? If you wanted to “integrate them together” you’d have to divide and multiply by some other differential:

VdP = V(dP/dt)dt, PdV= P(dV/dt)dt

int((VdP/dt + PdV/dt)dt)

You can’t integrate with respect to two different things at once, what would the limits be?