Chapter 6 Additional Integration Topics Section R Review

Chapter 6 Review Important Terms, Symbols, Concepts 6.1 Area Between Curves If f and g are continuous and f(x) > g(x) over the interval [a, b], then the area bounded by y = f (x) and y = g(x) for a < x < b is given by

Chapter 6 Review 6.1 Area Between Curves (continued) A graphical representation of the distribution of income among a population can be obtained by plotting data points (x,y) where x represents the cumulative percentage of families at or below a given income level, and y represents the cumulative percentage of total family income received. Regresssion analysis can be used to find a function called a Lorenz curve that best fits the data.

Chapter 6 Review 6.1 Area Between Curves (continued) A single number, the Gini Index, measures income concentration: Gini Index = A Gini index of 0 indicates absolute equality - all families share equally in the income. A Gini index of 1 indicates absolute inequality - one family has all of the income and the rest have none.

Chapter 6 Review 6.2 Applications in Business and Economics Probability Density Functions. If any real number x in an interval is a possible outcome of an experiment, then x is said to be a continuous random variable. The probability distribution of a continuous random variable is described by a probability density function f that satisfies f (x) > 0 for all real x. The area under the graph of f (x) over the interval (–∞, ∞) is exactly 1. The probability that c < x < d is

Chapter 6 Review 6.2 Applications (continued) Continuous Income Stream. If the rate at which income is received - its rate of flow - is a continuous function f (t) of time, then the income is said to be a continuous income stream. The total income produced by a continuous income stream from t = a to t = b is The future value of a continuous income stream that is invested at rate r, compounded continuously for 0 < t < T, is

Chapter 6 Review 6.2 Applications (continued) Consumers’ and Producers’ Surplus. If is a point on the graph of a price-demand equation p = D(x), then the consumers’ surplus at a price level of is Similarly, for a point on the graph of a price-supply equation p = S(x), the producers’ surplus at a price level of is

Chapter 6 Review 6.3 Integration by Parts Some indefinite integrals, but not all, can be found by means of the integration by parts formula: Select u and dv with the help of the guidelines in the section. 6.4 Integration Using Tables A table of integrals is a list of integration formulas that can be used to find indefinite or definite integrals of frequently encountered functions. Such a list appears in Table II of Appendix C.