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If f(x) is an anti-derivative (i.e. primitive) of x*e^(-x^2) and f(0)=1. Then f(1)=?

  • Math -

    let u = x^2
    we have
    f = 1/2∫e^-u du
    f(x) = -1/2 e^(-x^2) + C

    1 = -1/2 (1) + C
    C = 3/2

    f(x) = -1/2 e^(-x^2) + 3/2
    f(1) = -1/2 * 1/e + 3/2
    = 1/2 (3 - 1/e)

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