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Laplace Transformations help me please?

  1. Dec 3, 2009 #1
    Laplace Transformations.... help me please?

    1. The problem statement, all variables and given/known data.

    Find the laplace transformations of the following:

    a. [tex]
    \sin\, {\sqrt\,{x}}
    [/tex]

    b. [tex]
    \frac{\cos\,{\sqrt{x}}}{{\sqrt{x}}}
    [/tex]

    c. [tex]
    \ erf\,{(t)}^\frac{1}{2}}
    [/tex]

    d. [tex]
    \int_{t}^\infty\;\frac{\cos\,x}{x}\
    [/tex]

    e. [tex]
    \int_{t}^\infty\;\frac{{e}^{-x}}{x}\
    [/tex]


    2. Relevant equations.





    3. The attempt at a solution


    I used some properties of Laplace transformations, integration methods but still, didn't work.
     
    Last edited: Dec 3, 2009
  2. jcsd
  3. Dec 3, 2009 #2
    Re: Laplace Transformations.... help me please?

    are you sure about interval in prob d. and e.? I think it should be [t, inf].
     
  4. Dec 3, 2009 #3
    Re: Laplace Transformations.... help me please?

    yeah... sorry typographical error.. It should be from t to infinity. Thanks!
     
  5. Dec 3, 2009 #4
    Re: Laplace Transformations.... help me please?

    +++ For (d):
    You have f(t) ==> f'(t) = -cost / t ==> tf'(t) = -cost
    Now, find Laplace transform in both side and use final theorem, differentiation properties to find F.

    +++ (e) is similar to (d)

    p/s: trying to solve (a) :(
     
  6. Dec 3, 2009 #5
    Re: Laplace Transformations.... help me please?

    d is called cosine integral right?

    and e is exponential integral?
     
  7. Dec 3, 2009 #6
    Last edited by a moderator: Apr 24, 2017
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