Chapter 14 Review Important Terms, Symbols, Concepts

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Chapter 14 ReviewImportant Terms, Symbols,
Concepts

• 14.1 Area Between Curves
• If f and g are continuous and f(x) gt g(x) over
  the interval a, b, then the area bounded by y
  f (x) and y g(x) for a lt x lt b is given by

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Chapter 14 Review

• 14.1 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.

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Chapter 14 Review

• 14.1 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.

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Chapter 14 Review

• 14.2 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) gt 0 for all real x.
• The area under the graph of f (x) over the
  interval (-?, ?) is exactly 1.
• The probability that c lt x lt d is

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Chapter 14 Review

• 14.2 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 lt t lt T, is

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Chapter 14 Review

• 14.2 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

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Chapter 14 Review

• 14.3 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.
• 14.4 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.