integrated rate law

According to IUPAC Compendium of Chemical Terminology the rate law or rate equation for a chemical reaction is an equation which links the reaction rate with concentrations or pressures of reactants and constant parameters (normally rate coefficients and partial reaction orders). To determine the rate equation for a particular system one combines the reaction rate with a mass balance for the system . For a generic reaction A + B → C the simple rate equation (as opposed to the much more common complicated rate equations) is of the form:
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Rate laws like d[A]/dt = -k[A] give instantaneous concentration changes. To find the change in concentration over time, the instantaneous changes must by added (integrated) over the desired time interval. The rate law d[A]/dt = -k[A] can be integrated from time zero to time t to obtain the integrated rate law ln([A]/[A]o = -kt, where [A]o is the initial concentration of A.