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Math Help - Direct Integration

  1. #1
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    Direct Integration

    Calculate, using direct integration, the value of e^2t
    given that s > -2.

    and...

    e^t = 1/s-1
    for s > 1

    Any help on how to do this direct integration would be great guys, thank you
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  2. #2
    MHF Contributor matheagle's Avatar
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    s,t? Are you asking about LaPlace transforms?
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  3. #3
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    yes. sorry, i didnt put the laplace sign at the front
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  4. #4
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    Quote Originally Posted by tone999 View Post
    Calculate, using direct integration, the value of e^2t
    given that s > -2.

    and...

    e^t = 1/s-1
    for s > 1

    Any help on how to do this direct integration would be great guys, thank you
    By definition: LT[f(t)] = \int_0^{+\infty} e^{-st} f(t) \, dt.

    Therefore: LT\left[ e^{2t} \right] = \int_0^{+\infty} e^{-st} e^{2t} \, dt = \int_0^{+\infty} e^{-t(s-2)} \, dt .

    It's expected you can calculate an improper integral like this one.
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