Question

\int _{ -\infty }^{ \infty }{ \frac { { e }^{ -y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverge?

Answer 1

\[\int\limits _{ -\infty }^{ \infty }{ \frac { { e }^{ -y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverege? \]

Answer 2

Diverges because from minus infinity to zero the expression e^-y is much much larger than y^2+1. Actually because you take the integral from minus infinity to infinity this holds:\[\int\limits_{-\infty}^{\infty}\frac{ e^-y }{ y^2+1 }dy = \int\limits_{-\infty}^{\infty}\frac{ e^y }{ y^2+1 }dy \]

Answer 3

diverges. take simple example of \[\int\limits_{-infinity}^{infinity}(e^x)dx is \not convergent. and whether you divide \it by X^2 +1 .\]
that is a positive no....wont effect as we are talkin about infinity/infinty