I have a problem with the following exercise. I don't really have an idea where to start. I'm glad about every help. So here is the exercise:
Suppose $f\colon R \to R$ is a function in $L^1(R)$ (i.e integrable function). Show that $\lim_{n \to \infty}\int f(x)\sin(nx)dx=0.$
Thanks already for any help!