The tentative rate equation determined by the method of initial rates is therefore normally verified by comparing the concentrations measured over a longer time (several half-lives) with the integrated form of the rate equation; this assumes that the reaction goes to completion.
For example, the integrated rate law for a first-order reaction is
where  is the concentration at time  and  is the initial concentration at zero time. The first-order rate law is confirmed if  is in fact a linear function of time. In this case the rate constant  is equal to the slope with sign reversed.