Integral

Integral - Some Handy Integrals Gaussian Functions 1 1/2 2...

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Some Handy Integrals Gaussian Functions 0 e -ax 2 dx = 1 2 π a 1/2 0 x e -ax 2 dx = 1 2a 0 x 2 e -ax 2 dx = 1 4a π a 1/2 0 x 3 e -ax 2 dx = 1 2a 2 0 x 4 e -ax 2 dx = 3 8a 2 π a 1/2 0 x 5 e -ax 2 dx = 1 a 3 0 x 2n e -ax 2 dx = 1·3·5···(2n-1) 2 n+1 a n π a 1/2 0 x 2n+1 e -ax 2 dx = n! 2 1 a n+1 Exponential Functions 0 x n e -ax dx = n! a n+1 Integrals from - to : Even and Odd Functions The integral of any even function taken between the limits - to is twice the integral from 0 to . The integral of any odd function between - and is equal to zero, see Figure 1. 0 x -> even function integrals add odd function
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