# How to solve the following Riemann sum

Could someone explain step by step how to solve this Riemann sum: $$\frac{1}{n} \sum_{i=0}^n\left(\frac{k}{n}\right)^2\frac{1}{8}\arcsin\frac{k}{n}\frac{1}{2}$$ k/n inside the sum is all squared. I don't know what to do with that 1/2 and 1/8. I thought the integral would be something like $$x^2\arcsin\frac{x}{2}$$

• Should the sum be over $k$? – SEWillB May 12 '17 at 11:13
• yes I left it like that because I copied from the java help page,my bad – Lola May 12 '17 at 11:16

We have $\frac{1}{n} \sum_{i=0}^n\left(\frac{k}{n}\right)^2\frac18\arcsin\frac{k}{n}\frac{1}{2} \to \frac{1}{8} \int_0^1x^2\arcsin\frac{x}{2} dx$ for $n \to \infty$.