Question

differential equations

Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral **F¢)} = [" e stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. 16, f(t) = Ost<4 t24 Complete the integral(s) that defines {f(t)}. {f(t)} = o Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = (s > 0)

Answer 1

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explanation :

solution :- given ;- flt). :- La place transform of a L (flt)) function f(t) at .st our function flut) is defined defined as :- f(t) ost <4 &> 4. mords :- In other For t. between between to 4 2 flat ) =6. 4 to Infinity & ft) = 0 Calculate Laplace transform of Now So, the flt) So, L[814)] st e ftat From - o break Intregral into two parts. - 8t 4 e flt oft er CS Scanned til GamScanner 4 Now f ést fltoft

So, Now In & First Integral from put f(t) = 6, In second Integral from 4 Integral from 4 to Infinity put flt) = f(t) d t = 4 -Set -bt = si e-st 167dt e todt. o 14 Lif(t)) 6 - 8th alt fola olt. 2 PA Now Evaluate this Integral. Left) = be dt 14 st 4 CO 85 dt st 6 e -& 6 e teo Files edx 8 =en So, IL I-e 8 POR Answer ICS Scanned with CamScanner & Ine 48
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