Hi all,
I'll state the question, then explain my thinking.
Evaluate $\displaystyle \int_0^{\inf} [ H(t - \frac{\pi}{4}) - H(t)] \cos{2t}e^{-st} dt$ where $\displaystyle s > 0 $
Ok, I know the heaviside function limits the range between 0 and $\displaystyle \frac{\pi}{4}$.
I also know that the laplace transform of $\displaystyle \cos{2t}$ is $\displaystyle \frac{s}{s^2 + 4}$
What I don't know is how I'm meant to effectively combine these properties together to correctly evaluate the integral.
Any help would be greatly appreciated.