Recent content by lwebb

I apologise in advance if this is a stupid question, but could one say that the two expressions are different because the infinities in the first expression may or may not be of the same magnitude, and so the area under curve is therefore undefined. Whereas the infinities in the second...

What is the difference between \int_{-\infty}^{\infty} \frac{x}{1+x^2}dx and \lim_{R\rightarrow \infty}\int_{-R}^{R} \frac{x}{1+x^2}dx ? And why does the first expression diverge, whilst the second converges and is equal to zero?