# Laplace Transform of Product of Two Functions

1. Dec 12, 2011

### trust

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

Laplace Transform of u(t-∏/2)et

(u is unit step function)

2. Relevant equations

Laplace Transform Table (any)

3. The attempt at a solution

I tried using the Laplace transform for the unit step function and the exponential function.

L{u(t-∏/2)} = e-(∏s)/2

L{et} = 1/(s-1)

L{u(t-∏/2)et} = (e-(∏s)/2)(1/(s-1))

When I check my answer this is all correct except I'm missing an e∏/2 term. (The correct answer is (e-(∏s)/2)(1/(s-1))(e∏/2). Does anyone know where this extra term comes from?

2. Dec 12, 2011

### LCKurtz

I assume you have the formula$$\mathcal L(f(t-a)u(t-a) = e^{-as}\mathcal Lf(t)$$Write your function as$$e^{(t-\frac \pi 2)}e^{\frac \pi 2}$$and use that.

3. Dec 12, 2011

### Ray Vickson

The Laplace transform of a product is NOT the product of the transforms. Why don't you just do the problem directly: u(t - π/2) is 0 for t < π/2 and 1 if t > π/2, so you just have a simple integral of an exponential.

RGV

4. Dec 12, 2011

### trust

Thanks, I got it now. I was thinking that the transform of the product was the product of the transforms.

Last edited: Dec 12, 2011