Finding Limit of a Certain Integral – math.stackexchange.com

Suppose $f:[a,b]\to\mathbb{R}$ is continuous. Determine if the following limit exists $$\lim_{n\to\infty}\int_a^b f(x)\sin^3{(nx)} \:dx.$$ As $f(x)$ and $\sin^3{(nx)}$ are continuous, so their ...

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