(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

My professor gave us this problem:

Convert the limit to an integral:

[tex]\lim_{n\rightarrow inf} \frac{1}{n}(\sin(\pi/2) + \sin(\pi/2) + ... + \sin(\pi))[/tex]

he said it was right endpoint from [0,π]

then he set Δx = [itex]\frac{\pi}{n}[/itex]

then

[tex] \lim_{n\rightarrow inf} \frac{1}{\pi}(\frac{\pi}{n} \sum_{i=1}^{n} \sin(\frac{i\pi}{n}))[/tex]

[tex] = \frac{1}{\pi} \int\limits_{0}^{\pi}\sin{x}\, dx[/tex]

[tex] = \int\limits_{0}^{1}\sin{x}\, dx [/tex]

I just don't understand how he found Δx as being π/n or how he munipulated the formula to get the limits for the inetgral.

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Can someone explain this proccess for expressing limits as an integral?

**Physics Forums | Science Articles, Homework Help, Discussion**