Integration Formula Definitions and Examples

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Integration Formula Definitions and Examples

Integration Formula

Indefinite integral

integral sin(x) dx = -cos(x) + constant

Plots of the integral

Alternate form of the integral

-1/2 e^(-i x) - e^(i x)/2 + constant

Series expansion of the integral at x = 0

-1 + x^2/2 - x^4/24 + O(x^6)
(Taylor series)

Definite integral over a half-period

integral_0^π sin(x) dx = 2

Definite integral mean square

integral_0^(2 π) (sin^2(x))/(2 π) dx = 1/2 = 0.5

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