How to find La Place transform of cos(x) * unit step function (x - pi)

[lonewolf219]

Homework Statement

Find the La Place transform of cos(x)*(u(x-\pi))

Homework Equations

L{u(t-a)}(s)=(e^(-as))/s

The Attempt at a Solution

I don't think I can just multiply this by the La Place transform of cos (x), which is s/(s^2) ?

 

[lonewolf219]

I apologize if I am posting in the wrong forum..

 

[MisterX]

You're right, you wouldn't be able to just multiply the Laplace transforms together. You can write out the integral, and use the unit step to change the limits of integration. Then, you can solve it by integration by parts, I think.

 

[LCKurtz]

You might use$$
\mathcal L(f(t)u(t-a)) = e^{-as}\mathcal L(f(t+a))$$

 

[lonewolf219]

Thanks for both suggestions! I appreciate the help