# Midterm coming up! one question

• Oct 8th 2008, 07:28 AM
3deltat
Midterm coming up! one question
For study for the review, we recieved a couple questions. However, I got stuck on this. if you can help then itd be real awesome...

The integral of x / (1 + x^4), from 1 to infinity... find convergance...
• Oct 8th 2008, 07:38 AM
ThePerfectHacker
Quote:

Originally Posted by 3deltat
For study for the review, we recieved a couple questions. However, I got stuck on this. if you can help then itd be real awesome...

The integral of x / (1 + x^4), from 1 to infinity... find convergance...

$\int \limits_1^{\infty} \frac{x}{x^4+1} dx = \frac{1}{2} \int \limits_1^{\infty} \frac{(x^2)'}{(x^2)^2+1}dx = \frac{1}{2} \int \limits_1^{\infty} \frac{d\mu }{\mu^2 +1} = \frac{\pi}{4}$

Not only did we show it converges we showed what the value is.