improper integral

Examples of improper integral in the following topics:

• Improper Integrals

  • Specifically, an improper integral is a limit of one of two forms.
  • First, an improper integral could be a limit of the form:
  • Second, an improper integral could be a limit of the form:
  • However, the improper integral does exist if understood as the limit
  • Evaluate improper integrals with infinite limits of integration and infinite discontinuity

• The Integral Test and Estimates of Sums

  • The integral test is a method of testing infinite series of nonnegative terms for convergence by comparing them to an improper integral.
  • The integral test for convergence is a method used to test infinite series of non-negative terms for convergence.
  • The infinite series $\sum_{n=N}^\infty f(n)$ converges to a real number if and only if the improper integral $\int_N^\infty f(x)\,dx$ is finite.
  • In other words, if the integral diverges, then the series diverges as well.
  • The integral test applied to the harmonic series.

• Comparison Tests

  • The limit comparison test is a method of testing for the convergence of an infinite series, while the direct comparison test is a way of deducing the convergence or divergence of an infinite series or an improper integral by comparison with other series or integral whose convergence properties are already known.
  • The direct comparison test provides a way of deducing the convergence or divergence of an infinite series or an improper integral.
  • In both cases, the test works by comparing the given series or integral to one whose convergence properties are known.

• Absolute Convergence and Ratio and Root Tests

  • Similarly, an improper integral of a function, $\textstyle\int_0^\infty f(x)\,dx$, is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if $\int_0^\infty \left|f(x)\right|dx = L$.

• Rituals

  • Physical preservation of these monuments would damage the spiritual and cultural integrity of both this process and its purpose.
  • Cultural integrity can be compromised or wrongfully preserved through improper association in a museum context.
  • For example, when books are piled on top of a Qur'an in a museum display the spiritual integrity is compromised or destroyed completely, leaving the physical object devoid of cultural meaning .

• Honor and Violence

  • The South is said to have a "culture of honor," in which individuals avoid making unintentional insults and do not accept improper conduct.
  • The prevailing culture of the Southern United States is said to be a "culture of honor," where people avoid unintentional offense to others and maintain a reputation for not accepting improper conduct by others.
  • Because transaction costs were very high during this period, one had to be perceived as having personal integrity or character in order to be considered likely to honor one's contracts and debts.

• Evaluating Employee Performance

  • Detriments of the PA system include the possible hindrance of quality control, stress for both employees and management, errors in judgment, legal issues arising from improper evaluations, and the implementation of inappropriate performance goals.
  • There are various ways human resource professionals can approach assessing performance, though integrating various perspectives (i.e., collecting the most differentiated data) will paint the clearest picture.
  • 360-degree feedback: 360-degree feedback includes multiple evaluations of employees; it often integrates assessments from superiors and peers, as well as self-assessments.

• Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

  • Some problems with multiple regression include multicollinearity, variable selection, and improper extrapolation assumptions.
  • Examine how the improper choice of explanatory variables, the presence of multicollinearity between variables, and extrapolation of poor quality can negatively effect the results of a multiple linear regression.

• Barriers to Managing Control

  • Barriers to managing control include lack of resources, inaccurate measurements, improper information flow, and incorrect analyses.
  • Barriers to organizational control can include scarcity of resources, inaccurate measurements of the process, improper information flow, and incorrect analyses.

• Disruptive, Impulse-Control, and Conduct Disorders

  • The most effective treatment for an individual with conduct disorder is one that seeks to integrate individual, school, and family settings.
  • Several treatments currently exist, the most effective of which is multi-systemic treatment (MST), an intensive, integrative treatment that emphasizes how an individual's conduct problems fit within a broader context.
  • Lesions in these areas are also associated with improper blood sugar control, leading to decreased brain function in these areas, which are associated with planning and decision making.