How to solve this limit, hint only $$\lim_{n\to\infty}\bigg(\frac{1}{\sqrt{9n^2-1^2}}+\frac{1}{\sqrt{9n^2-2^2}}+ \dots +\frac{1}{\sqrt{9n^2-n^2}}\bigg)$$ I need a hint. I see that maybe compute with integral. But what the integrable function?

Hint Since you ask for a simple hint then: Use a Riemann sum and compute this integral
$$\int_0^1\frac{dx}{\sqrt{9-x^2}}$$
