Ingram Pritchard
08/14/2023 · High School
10. If \( f(t) \) is continuous for \( t \geqslant 0 \), the Laplace transform of \( f \) is the function \( F \) defined by the improper integral: \[ F(s)=\int_{0}^{\infty} f(t) e^{-s t} d t \] where \( s \) is a constant taken from the set of values for which the integral converges. Assuming that \( s>0 \), find the Laplace transform \( F(s) \) of the function \( f(t)=t \).
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The Laplace transform of \( f(t) = t \) is \( \frac{1}{s^2} \).
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