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Math Help - Simpl-integral

  1. #1
    Super Member dhiab's Avatar
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    Simpl-integral

    If :

    Calculate :
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  2. #2
    Super Member Random Variable's Avatar
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    let  I(b) = \int^{\infty}_{-\infty} e^{bt} f(t) \ dt

    then  I'(b) = \int^{\infty}_{-\infty} t e^{bt} f(t) \ dt

    and  I'(0) = \int^{\infty}_{-\infty} t f(t) \ dt = \frac{d}{db} \arcsin \Big( b- \frac{1}{\sqrt{2}} \Big) evaluated at  b = 0

     = \sqrt{2}
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