chi sann

chi sann

Answered question

2022-05-04



Answer & Explanation

xleb123

xleb123

Skilled2023-05-04Added 181 answers

To find the Laplace transform of f(t)=t2t2, we use the definition of the Laplace transform and the properties of the transform. The Laplace transform of f(t) is given by:
{f(t)}=0estf(t)dt
Substituting the expression for f(t), we get:
{f(t)}=0est(t2t2)dt
We can split this integral into three parts:
{f(t)}=0estt2dt0esttdt0est2dt
Using the formula for the Laplace transform of tn, we get:
{tn}=n!sn+1
Applying this formula to the first integral, we get:
0estt2dt=2!s2+1=2s3
Using the same formula for the Laplace transform of tn, we get:
{t}=1s2
Applying this formula to the second integral, we get:
0esttdt=1s2
For the third integral, we can use the formula for the Laplace transform of a constant function:
{c}=cs
Therefore, we have:
0est2dt=2s
Putting it all together, we get:
{f(t)}=2s31s22s
Hence, the Laplace transform of f(t)=t2t2 is:
{f(t)}=2s31s22s

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