How Do You Solve a Piecewise Laplace Transform When f(t)=t?

[Will_M]

Homework Statement

This is my first post, so bear with me. I have seen others who have posted their questions and the problem looked like it was typed in mathcad or something. How do I do that?

Ok so I'm trying to figure out how to solve a piecewise Laplace transform when f(t)=t

the actual problem is

f(t)={t, 0<t<1 (should be read as 0 less than or equal to t...)
{1, t>1 (should be read as t greater than or equal to 1)

Homework Equations

L{f(t)}= integral of e^-stf(t)dt

The Attempt at a Solution

My attempt. Please help me figure out how I can make this show up as it would in person. (with the integral sign, exponents, etc.)

=integral from 0 to 1 of e^-sttdt + integral from 1 to infinity of e^-stdt

=-1/s(e^-s)(1/2) + 1/s(e^-s)

=(-e^-s/2) + ((1/s)e^-s)


the correct answer should be =(1/s²) - (e^-s/s²)

I appreciate the patience everyone.

 

[Will_M]

wait wait don't tell me. I've almost got it.

 

[Will_M]

I'm an idiot and forgot basic calculus rules.

/thread