Compute the Laplace transform of f(t)={(8 ,if 0 <= x <14),(9t,if 14 <= x <infty):}

chillywilly12a 2021-09-09 Answered

Compute the Laplace transform of f(t)={8if 0x<149tif 14x<

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Expert Answer

Usamah Prosser
Answered 2021-09-10 Author has 86 answers

Step 1
Consider the given information.
f(t)={8if 0x<149tif 14x<
The Laplace transform is defined as,
F(s)=0estf(t)dt
Put the value in the integral.
L{f}(s)=014est8dt+14est(9t)dt
=8014estdt+914testdt
Step 2
Consider the values for integration as,
u=t,dv=est
du=1,v=ests
Put the values in the function.
L{f}(s)=8014est+914test
=8[ests]014+9[tests]14+1s14estdt
=8(e14s1)s9[tests]1491s[ests]14
=8(e14s1)s+(126s+9)e14ss2
=118e14ss+8s+9e14ss2

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