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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