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Asked Jul 8, 2019
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Use the definition of Laplace Transforms to show that:

ms to show that
n!
L{t"} = s+1 n = 1,2,3, ...
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ms to show that n! L{t"} = s+1 n = 1,2,3, ...

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Expert Answer

Step 1

Given:

The laplace transformation,

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n! L{r} n+1 S

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Step 2

Proof:

Consider L(tn) and simplify it as follows.

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L{=f 0 L{r}=je()dt Apply intergration by parts, v u Ju'v Here, dv e -st u =t -st n+1 du nt" S -st -st n-1 dt S 0 n-1 -st =0+ 0

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Step 3

Now substitute the values 1, 2, ...

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When n 1 L ()7{}7 11 When n 2 1 2 2!

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