Abstract
This chapter discusses the applications of the definite integral to problems in business, economics, motion, biology, consumption of natural resources, and probability. These applications are based on an important relationship between the change in the value of a function and the definite integral of its derivative. The marginal cost (MC), marginal revenue (MR), and marginal profit (MP) are the derivatives of the cost function, revenue function, and profit function, respectively. An equation that involves an unknown function and its derivatives is called a differential equation. The differential equations arise in a variety of important applications, especially those involving rates of change. A function that satisfies a differential equation is called a solution of that equation. A condition that specifies the value of y for some specific value of x is called an initial condition, and the problem of solving a differential equation subject to an initial condition is called an initial value problem.
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