# Step function/laplace transform help

I didn't know how to do a 3 part piecewise function in latex, but I have f(x) defined as

$$0, t<0$$

$$t-\Pi , \leq t < 2\Pi$$

$$0, t \geq 2\Pi$$

And I'm supposed to find the laplace transform of it. So I find the step function:

$$h(t) = u_{\Pi} (t- \Pi) - u_{2 \Pi}(t-2 \Pi)}$$

So, Tom, if I need 3 integrals I guess I've already gone astray, what happened?
EDIT: I think I might see what went wrong, This step function defines

$$0, t<0$$

$$t-\Pi , \leq t < 2\Pi$$

$$1, t \geq 2\Pi$$

pigs might fly?

in which case I need

$$h(t) = u_{\Pi} (t- \Pi) - u_{2 \Pi}(t)} - u_{2 \Pi}(t-2 \Pi)}$$

I'm suspicious of the middle term.

Last edited:

Tom Mattson
Staff Emeritus