I recently started reading Feynman Lectures on Physics (Vol 1). I came across the formula for work done as,
Work done is $\int\vec{F}\cdot d\vec{s}$
My question is:
What does $\int\vec{s}\cdot d\vec{F}$ represent?
Does it even make sense to calculate the product of total displacement and small amount of force?
or does $\int\vec{F}\cdot d\vec{s}$ have the same meaning as $\int\vec{s}\cdot d\vec{F}$, they both represent the work done?