Convolution theorem property about signals

[jaus tail]

Homework Statement

Homework Equations

Laplace and then inverse laplace.

The Attempt at a Solution

Laplace of U(t-t_o) = 1/s e^(-t_os)
x(t)-->X(s)
Laplace inverse
1/s means integration.
e^(-t_os) means delay on x(t) by t_o.
I think answer should be C
Book answer is D.
How am I wrong?

 

[scottdave]

Perhaps look at it from the definition of Convolution rather than going through the Laplace transform.
https://en.m.wikipedia.org/wiki/Convolution

I'm on my phone, so the link is the mobile Wikipedia

 

[jaus tail]

I'm struggling to understand it. Is book answer right? I got an exam on on 10th feb on 10 engineering subjects, thus am rushing through the questions and answers.

 

[jaus tail]

I replaced x(t) by t² and got the answer as C.
First I laplace transformed x(t) as 2!/s³
Laplace of u(t-t0) = e^-t₀s
Multiplied laplace
Used inverse transform
to get:
(t-to)³ the whole divided by 3
And used trial and error method to see which option matches this.
C is right answer.