# Crazy double integral

1. Oct 23, 2006

### glid02

Here's the question:

We want to evaluate the improper integral
[Broken]

Do it by rewriting the numerator of the integrand as [Broken] 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.

Last edited by a moderator: Apr 22, 2017 at 1:35 PM
2. Oct 23, 2006

### 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.