text{Laplace transforms A powerful tool in solving problems inengineering and physics is the Laplace transform.

Chesley 2021-03-02 Answered

Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by 
(F(s)=0estf(t)dt
where we assume s is a positive real number. For example, to find the Laplace transform off(t)=et , the following improper integral is evaluated using integration by parts:
F(s)=0estetdt=0e(s+1)tdt=1s+1
 Verify the following Laplace transforms, where u is a real number. 
f(t)=tF(s)=1s2

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Expert Answer

AGRFTr
Answered 2021-03-03 Author has 95 answers

Step 1
Here, the objective is to prove that  L(t)=1s2
Step 2
Let f(t) be t
Laplace transformation of f(t) is defined as:
L(t)=F(s)=0estf(t)dt
Substitute f(t)=t
L(t)=F(s)=0esttdt
\(\text{Use integration by part } \int fg=fg-int

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