List of definite integrals

In mathematics, the definite integral:

is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.

The fundamental theorem of calculus establishes the relationship between indefinite and definite integrals and introduces a technique for evaluating definite integrals.

If the interval is infinite the definite integral is called an improper integral and defined by using appropriate limiting procedures. for example:

The following is a list of the most common definite Integrals. For a list of indefinite integrals see List of indefinite integrals.

Definite integrals involving rational or irrational expressions

Definite integrals involving trigonometric functions

(see Dirichlet integral)

Definite integrals involving exponential functions

(see also Gamma function)
(the Gaussian integral)
(where !! is the double factorial)


Definite integrals involving logarithmic functions

Definite integrals involving hyperbolic functions

Miscellaneous definite integrals

See also

References

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