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Useful Definite Integrals


There are some functions whose antiderivatives cannot be expressed in closed form. However, the values of the definite integrals of some of these functions over some common intervals can be calculated. A few useful integrals are given below.



Gamma function:

Gamma function maths

Gaussian integral:

gaussian integral math

bernoulli number in math integrals

math useful definite integral
math definite integral of sinc(x)

definite integral

(where Γ(z) is the Gamma function)

other useful definite integral

definite integral

(where I0(x) is the modified Bessel function of the first kind)

maths useful definite integral

The method of exhaustion provides a formula for the general case when no antiderivative exists:

The method of exhaustion provides a formula for the general case when no antiderivative exists



Find the integral of any function using our Integral Calculator

Find out the value of the integral of a function covering any interval using our Definite Integral Calculator




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