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Math Help - Semi urgent - Laplace Transform

  1. #1
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    Semi urgent - Laplace Transform

    Hi all,

    I'll state the question, then explain my thinking.

    Evaluate  \int_0^{\inf} [ H(t - \frac{\pi}{4}) - H(t)] \cos{2t}e^{-st} dt where  s > 0

    Ok, I know the heaviside function limits the range between 0 and \frac{\pi}{4}.

    I also know that the laplace transform of \cos{2t} is \frac{s}{s^2 + 4}

    What I don't know is how I'm meant to effectively combine these properties together to correctly evaluate the integral.

    Any help would be greatly appreciated.
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  2. #2
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    Your integral is equal to \int_0^{\pi/4}- \cos(2t)\,e^{-st} \,\mathrm{d}t is it not?
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  3. #3
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    I can see how the heaviside function can produce the new limits, however I can't see how you got the negative out the front of the variable and I'm unsure of what to do with it from there.
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  4. #4
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    Actually, I think I use this from the table of integrals to produce the answer from the above...




    But again I'm unsure how you got that negative out the front.
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  5. #5
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    What value does H(t-\pi/4) - H(t) have on the interval [0,pi/4]?

    From there, use integration by parts I think.
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  6. #6
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    Ah ok, -1 obviously. Thanks.
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