Finding Bounds of Integration for Integral of Cos(2+x)

[Qube]

Homework Statement

http://i.minus.com/jJQzZXoxXFqEB.png

Homework Equations

(b-a)/n = Δx

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?

 

[LCKurtz]

Homework Statement

http://i.minus.com/jJQzZXoxXFqEB.png

Homework Equations

(b-a)/n = Δx

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 number apart, right?

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

 

[Dick]

Homework Statement

http://i.minus.com/jJQzZXoxXFqEB.png

Homework Equations

(b-a)/n = Δx

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 number apart, right?

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?

 

[Qube]

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

I'm going from 1/n to 1.

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?

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.

 

[LCKurtz]

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

 

[Qube]

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

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

 

[LCKurtz]

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

Right. You know, it's not that hard to write math symbols on this forum. You ought to take a look at:

https://www.physicsforums.com/showpost.php?p=3977517&postcount=3