Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.2 The Existence of the Laplace Transform and the Inverse Transform - True-False Review - Page 685: d

False

Let us consider that the function $f$ is periodic function with period $T$ . $f(t+T)=f(t)$ Now, $f(t+T)=\sin (t+T)^2=\sin (t^2+2 \pi)$ Also, $(t+T)^2=t^2 +2 \pi\\ t^2+2tT+T^2=t^2+2 \pi \\ 2tT+T^2 =2 \pi$ Therefore, the given statement is $\bf{False}$.