Thanks for replying,I finally solve it through help of dr.math(http://mathforum.org/dr.math/)
Break the inteval [0,x] to [0,a] + [a,x].
$$
T(x)=\int_{0}^{x}\frac{dt}{1+t^{2}}=
\int_{0}^{a}\frac{dt}{1+t^{2}}+\int_{a}^{x}\frac{dt}{1+t^{2}}
$$
For the first inteval [0,a], $$...
Homework Statement
From introduction to analysis,by Arthur P. Mattuck,problem 20-1.
Problems 20-1
One way of rigorously defining the trigonometric functions is to start with the definition of the arctangent function. (This is the route used for example in the classic text Pure Mathematics by...
Homework Statement
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/" title="arctangent by gnu is not unix, on Flickr"><img...