Calculate the Laplace transform L\{f\} of the function f(t)=e^{4t+2}-8t^6+8 \sin (2t)+9 using the basic formulas

OlmekinjP 2021-09-15 Answered

Calculate the Laplace transform L{f} of the function f(t)=e4t+28t6+8sin(2t)+9 using the basic formulas and the linearity of the Laplace transform

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Expert Answer

Nathanael Webber
Answered 2021-09-16 Author has 117 answers

Step 1
f(t)=e4t+28t6+8sin(2t)+9
F(t)=e2e4t8t6+8sin(2t)+9
L{f(t)}=L{e2e4t8t6+8sin(2t)+9}
Apply linearity
L{f(t)}=e2L{e4t}8L{t6}8L{sin(2t)}+9L{1}
using the basic formulas
L{eat}=1sa,L{1}=1s
L{tn}=n!sn+1
and L{sin(at)}=as2+a2
So, L{f(t)}=e21s486!s782s2+22+91s
L{f}=e2s45760s716s2+22+9s

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