List of definite integrals

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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[edit]

Definite integrals involving trigonometric functions[edit]

(see Dirichlet integral)

Definite integrals involving exponential functions[edit]

(see also Gamma function)
(the Gaussian integral)
(where !! is the double factorial)
(where is Euler–Mascheroni constant)

Definite integrals involving logarithmic functions[edit]

Definite integrals involving hyperbolic functions[edit]

Frullani integrals[edit]

See also[edit]