# Why is it called an 'integral' curve?

The concept of a integral curve is relatively easy to understand as path through a vector field which is tangent to the field at each point.

But why is it called an "integral" curve? It appears to have little to do with integers, or integration.

• @apkg The standard example of a non-integrable equation is this: Can you find smooth surfaces in $\Bbb R^3$ on which we have $dz-x\,dy = 0$ at each point? (Curves are never a problem, at least locally.) Jan 18 at 3:20