Limits & Riemman Sum

1. May 5, 2008

lLovePhysics

1. The problem statement, all variables and given/known data
Question regarding #16

2. Relevant equations

Riemman Sum

3. 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

2. May 5, 2008

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: May 5, 2008
3. May 6, 2008

lLovePhysics

Well, here's what I have so far:

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

4. May 6, 2008

HallsofIvy

Staff Emeritus
So what part of that sum is dx and what part is f(x)? After you know f(x), what is its integral?