## David.Butler \int _{ -\infty }^{ \infty }{ \frac { { e }^{ -y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverge? one year ago one year ago

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1. David.Butler

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

2. Topi

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:$\int\limits_{-\infty}^{\infty}\frac{ e^-y }{ y^2+1 }dy = \int\limits_{-\infty}^{\infty}\frac{ e^y }{ y^2+1 }dy$

3. gvatsa212

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