3please show written work if possible Let f(t) be a function on [0, ∞). The Laplace transform of f is the function F defined by the integral F(s) = estf(t)dt. Use this definition to determine the Laplace transform of the following function.0f(t)=te-2t00The Laplace transform of f(t) is F(s) = (Type an expression using s as the variable.)It is defined for s>. (Type an integer or a fraction.)

Solution :- The given function is f(t) = te-2t then , we have…

Answered: Let f(t) be a function on [0, ∞o). The…

Advanced Engineering Mathematics

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ISBN:9780470458365

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Chapter2: Second-order Linear Odes

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Let f(t) be a function on [0, ∞o). The Laplace transform of f is the function F defined by the integral F(s) = 0 f(t)=te-2t estf(t)dt. Use this definition to determine the Laplace transform of the following fun