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The scientific substantiations of quality have been applied to models that pertain to mathematical statistics, the probability theory, the information theory, fuzzy systems, graphic methods, time series, and algebraic and numerical methods. To these, this article aims to present a new method of applying mathematical modelling in an economy based on knowledge, by using the concept of the definite integral, the composite function, and mathematical optimisation. The research methods used in the realisation of this article are bibliographic research, creation of new models, and problem-solving. Mathematical modelling, the simulation of the quality of life, etc. are methods and techniques of both theoretical and practical scientific approach, which are likely to lead to a better understanding of the role of quality in this field, as well as leading to the sustainable development of quality by providing new practical solutions to achieve a quality, always superior to the one obtained previously. In this article, the author presents some personal contributions to the scientific approach to quality, through modelling and simulation of the quality of life, and management of the quality of life in an economy based on knowledge.