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Let f(t) be a function on [0, 0). The Laplace transform of fis the function F...

Question:

Let f(t) be a function on [0, 0). The Laplace transform of fis the function F defined by the integral F(s) = S e-stat)at. Use

Let f(t) be a function on [0, 0). The Laplace transform of fis the function F defined by the integral F(s) = S e-stat)at. Use this definition to determine the Laplace transform of the following function. 0 € 5 0<t<3 f(t) = 2 3<t 2 and F(s) = 3+ - 15 otherwise The Laplace transform of f(t) is F(s) = for all positive st[ (Type exact answers.)

Answers

0 <t <3 31 2 3t -St FIS ) = flt) at . Te Te سا -st. est st + = dt © 2 dt حر -15-5) t -st +216 at +2 dt - در) 0 3 -(5-5) e + 2- (35-15) 1 1 5 -35 2 e S А s-5 15-5) I - 35 xe e + -35 2 e S a st $-5 (5-5) IS e - 35 e 2 + + - st (5-5) S-5 S -35 e IS e (Sat s- И atherwise fram eqh -35 e 5 + 2 (8:55 1 te-135-15) (95-15} ] [1+ s +13)° +13)*+...] + -35 2 e (-5)/2 + ess at 5=5 @ 15

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