^{8}Recall from the previous section (“The Concept of Differentiation”) that velocity could be defined as
the time-derivative of position: v = dx
dt All we have done here is algebraically solved for changes in x by first
multiplying both sides of the equation by dt to arrive at dx = v dt. Next, we integrate both sides of the equation in
order to “un-do” the differential (d) applied to x: ∫
dx = ∫
v dt. Since accumulations (∫
) of any differential
(dx) yields a discrete change for that variable, we may substitute Δx for ∫
dx and get our final answer of
Δx = ∫
v dt.