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    Improper Integral

    Indefinite integral

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

    Plots of the integral

    Plots of the integral

    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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