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Math Help - Laplace

  1. #1
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    Lightbulb Laplace

    Laplace-lapalce.jpg
    COULD YOU SHOW ME THE STEP BY STEP SOLUTION IN HOW THE UPPER FUNCTION (1/T)SIN(AT)BECOME THE LAPLACE OF LOWER FUNCTION ARCTAN(A/S)


    plsssssssssssssssss I REALY NEED IT FOR MAY ADVANCE MATH SUBJECT
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  2. #2
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    Re: Laplace

    L\left\{\frac{1}{t}\sin(\alpha t)\right\} = \int_0^\infty e^{-st}\frac{1}{t}\sin(\alpha t) dt

    Do integration by parts with the two functions u(t)=e^{-st} and v'(t)=\frac{\sin(\alpha t)}{t}

    You could also try this: rewrite the above integral as \int_0^\infty e^{-st}\frac{1}{t}e^{i\alpha t} dt, solve and take the imaginary part of your answer.
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  3. #3
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    Re: Laplace

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