# How to prove the definition of arctangent function using integral?

1. Oct 15, 2012

### zhongbeyond

1. The problem statement, all variables and given/known data
This is a problem from Introduction to Analysis by Arthur P. Mattuck,chapter 20,problem 20-1.

<a href="http://www.flickr.com/photos/86024731@N04/8090259684/" [Broken] title="arctangent by gnu is not unix, on Flickr"><img src="http://farm9.staticflickr.com/8193/8090259684_a5ce06801e.jpg" width="500" height="325" alt="arctangent"></a>

I have worked out question (a),(b),(c),but I am stucked in question (d).
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 6, 2017
2. Oct 15, 2012

### jambaugh

For d.) you will need to compare the given integral to the integral of some other function which you can show (easily) has limiting value < or = to 2.5 at infinity.
Suggestion: consider changing the numerator to make it integrable. Be sure to check that your comparison function is everywhere bigger. (You may need to use some glue.)