determine the Laplace transform of f. f{{left({t}right)}}={3}{t}{e}^{ -{{t}}}

Aneeka Hunt 2020-12-15 Answered
determine the Laplace transform of f.
f(t)=3tet
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Expert Answer

Laaibah Pitt
Answered 2020-12-16 Author has 98 answers
Step 1
To determine:
The Laplace transformation of the function f(t)=3tet
Formula Used:
F(s)=L(f(t))=0estf(t)dt
Step 2
Explanation:
Let f(t)=3tet
By using the formula,
F(s)=L(3tet)=0est3tetdt
=3limb0be(1s)ttetdt
=3limb[(t11se(1s)t)0b0b11se(1s)tdt]
=3(s+1)limb[(be(1s)b)0be(1s)tdt]
=3s+1limb0be(1s)tdt
=3s+1limb[1(s+1)e(1s)t]0b
=3(s+1)2limb[e(1s)b+1]
F(s)=3(s+1)2
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