# Limits & Riemman Sum

## Homework Statement

Question regarding #16

Riemman Sum

## The Attempt at a Solution

I know that the limit of the Riemman Sum is basically the integral. However, I do not know where to go from there. Do I need to use the Summation formulas? Thanks

## Answers and Replies

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rbj
can you write down the expression for a Riemann integral. something like:

$$\int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N ???$$

what goes in the question marks?

also, even though Riemann doesn't, assume things in the ??? are equally spaced. that's usually good enough.

Last edited:
can you write down the expression for a Riemann integral. something like:

$$\int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N ???$$

what goes in the question marks?

also, even though Riemann doesn't, assume things in the ??? are equally spaced. that's usually good enough.
Well, here's what I have so far:

$$\int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N (\frac{1}{N}\sin(\frac{\pi i}{N})$$

HallsofIvy