Answer:
1) [tex]L(y)=\frac{2}{s^{3}}[/tex]
2) [tex]L(y)=\frac{6}{s^{4}}[/tex]
Step-by-step explanation:
To find : Calculate the Laplace transforms of the following from the definition ?
Solution :
We know that,
Laplace transforms of [tex]t^n[/tex] is given by,
[tex]L(t^n)=\frac{n!}{s^{n+1}}[/tex]
1) [tex]y=t^2[/tex]
Laplace of y,
[tex]L(y)=L(t^2)[/tex] here n=2
[tex]L(y)=\frac{2!}{s^{2+1}}[/tex]
[tex]L(y)=\frac{2}{s^{3}}[/tex]
2) [tex]y=t^3[/tex]
Laplace of y,
[tex]L(y)=L(t^3)[/tex] here n=3
[tex]L(y)=\frac{3!}{s^{3+1}}[/tex]
[tex]L(y)=\frac{3\times 2}{s^{4}}[/tex]
[tex]L(y)=\frac{6}{s^{4}}[/tex]
