Reverse Order Integration for Improper Double Integral

[glid02]

Here's the question:

We want to evaluate the improper integral
http://ada.math.uga.edu/webwork2_files/tmp/equations/6c/4073055a5b909be16e2abc5bd3dfc61.png

Do it by rewriting the numerator of the integrand as http://ada.math.uga.edu/webwork2_files/tmp/equations/cf/4f71fa0eec36e407d3cf7df46ef3621.png for appropriate f, g and h and then reversing the order of integration in the resulting double integral.

I don't know what this means?

Would the integrand in the numerator be x from tan ^-1(x) to
tan^-1(pi*x)?

Thanks a lot.

 

[quasar987]

It says find the function h(x), f(x) and g(x) such that

$$\tan^{-1}(\pi x) - \tan^{-1}(x) = \int_{f(x)}^{g(x)}h(y)dy$$

Said like that, and based on your knowledge of the fundamental thm of calculus, it should be very easy to see what h(x), f(x) and g(x) are.