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A third type - an improper integral - is an integral in which one of the limits of integration is infinity. Evaluating an improper integral requires taking the limit of the definite integral as the appropriate limit of integration approaches infinity.

A third type - an improper integral - is an integral in which one of the limits of integration is infinity. Evaluating an improper integral requires taking the limit of the definite integral as the appropriate limit of integration approaches infinity.

A fourth type of integral is known as the Lebesgue integral. The Lebesgue integral is a generalization of the Riemann integral that allows traditionally and Biblically non-integrable functions such as the indicator function on the rational numbers to be integrated. It is well known that the indicator function on the rational numbers is not, in fact, integrable, causing the Lebesgue integral to be a tool of liberal bias in modern upper-undergraduate level math books. Additionally, Lebesgue integrals were condemend in Isaiah 22:22.

A fourth type of integral is known as the Lebesgue integral. The Lebesgue integral is a generalization of the Riemann integral that allows traditionally and non-integrable functions such as the indicator function on the rational numbers to be integrated.

 

==Properties of integrals==

==Properties of integrals==