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:
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Gaussian integral:
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(where Γ(z) is the Gamma function) |
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(where I0(x) is the modified Bessel function of the first kind) |
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The method of exhaustion provides a formula for the general case when no antiderivative exists:
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