# Laplace transform of a piecewise function

1. Apr 11, 2015

### Feodalherren

1. The problem statement, all variables and given/known data

f(t) = e^t when 0≤t<1
and 0 when t≥1

2. Relevant equations
Laplace transformations

3. The attempt at a solution

so the Laplace integral becomes

from 0 to 1 ∫e^(st^2)dt + 0

how do I integrate this?

2. Apr 11, 2015

### Rellek

Clarification:

Laplace transform or Lagrange Transform...?

3. Apr 11, 2015

### Feodalherren

4. Apr 11, 2015

### Rellek

Alright, let's do this:

From 0 to 1 we have one function, and from 1 onward we have another. Split up our integral as so:

$$\int_0^1 e^{-st} e^{t}dt + \int_{1}^{\infty} e^{-st}(0)dt \implies \int_0^1 e^{t(1-s)}dt$$

5. Apr 11, 2015

### Feodalherren

Wait a second, doesn't the part that goes from 1 to +infinity get canceled out because the integral becomes

∫ e^(-st) (0) dt = 0

?

6. Apr 11, 2015

### Rellek

Excuse my reading comprehension, I thought it said f(t) = 1. Corrected.

7. Apr 11, 2015

### Feodalherren

Ah now I see what I did wrong! DUH! Such a stupid mistake.

Thank you sir!

8. Apr 11, 2015

### SteamKing

Staff Emeritus
How did you get an integrand of est2 ?

Remember, ex ⋅ ey = e(x + y), not exy

9. Apr 11, 2015

### Feodalherren

I was just asking myself the same thing. I think I need to take a break. I've been doing math since 7.30 this morning. It's 1.30 pm now :).