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proof: $\lim_{n\rightarrow \infty } \int_{0}^{a}f(nx)dx = aL$ when $\lim{x\to\infty }f(x)= L$

we know that:

$\lim{x\to\infty }f(x)= L$

$\alpha > 0$

i need to prove that:

$\lim_{n\rightarrow \infty } \int_{0}^{a}f(nx)dx = aL$

my idea was to get the limit inside the integral and then i will have this:

$\int_{0}^{a}L = L(a-0)$

but i am not sure that it is correct

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