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Math Help - laplace transform

  1. #1
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    laplace transform

    I have to find the laplace transform of the intrgral from 0 to (t-a) of f(u) du in terms of F(p) = laplace(f(t))

    Do i use the convolution theorem where g(u) = 1

    but even if i do that teh convolution theorem is the laplace of intregral from 0 to t of (f(t-u)g(u)) = F(p)G(p)

    G(p) in our case would be 1/p?
    but I dont know what to do with the (t-a)
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  2. #2
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    Quote Originally Posted by CookieC View Post
    I have to find the laplace transform of the intrgral from 0 to (t-a) of f(u) du in terms of F(p) = laplace(f(t))

    Do i use the convolution theorem where g(u) = 1

    but even if i do that teh convolution theorem is the laplace of intregral from 0 to t of (f(t-u)g(u)) = F(p)G(p)

    G(p) in our case would be 1/p?
    but I dont know what to do with the (t-a)
    \int_0^{t - a} f(u) \, du is essentially a convolution of g(t) with 1 (change the variable of integration and it is obvious). And you are expected to know the Laplace transform of a convoution of two functions.
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