# Homework Help: Limits of Integration

1. Nov 22, 2013

### Qube

1. The problem statement, all variables and given/known data

http://i.minus.com/jJQzZXoxXFqEB.png [Broken]

2. Relevant equations

(b-a)/n = Δx

3. The attempt at a solution

I know how to express the sum as an integral .. almost. It is the integral of cos(2+x) with respect to x. However, what are my bounds of integration? I know that b-a must equal 1, but I don't think I can pick any arbitrary b and a that are just one counting number apart, right?

Last edited by a moderator: May 6, 2017
2. Nov 22, 2013

### LCKurtz

Write down the $x_i$ in this problem for $i=1..n$. That will give you an idea of what interval is being used.

Last edited by a moderator: May 6, 2017
3. Nov 22, 2013

### Dick

Of course, you can't. You are identifying i/n with x. What are the limits of i/n as i goes from 1 to n? Now what happens if you take the limit?

Last edited by a moderator: May 6, 2017
4. Nov 22, 2013

### Qube

I'm going from 1/n to 1.

It seems as if when I take the limit as n approaches infinity 1/n becomes 0. The limit of a constant is the constant, so it appears my interval is 0 to 1.

5. Nov 22, 2013

### LCKurtz

So the limit of that sum as $n\to \infty$ is ...?

6. Nov 22, 2013

### Qube

The integral of cos(2 + x) with respect to x and with bounds as 0 and 1.

7. Nov 22, 2013