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anonymous
 3 years ago
\int _{ \infty }^{ \infty }{ \frac { { e }^{ y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverge?
anonymous
 3 years ago
\int _{ \infty }^{ \infty }{ \frac { { e }^{ y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverge?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits _{ \infty }^{ \infty }{ \frac { { e }^{ y } }{ { y }^{ 2 }+1 } } converges \quad or\quad diverege? \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Diverges 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:\[\int\limits_{\infty}^{\infty}\frac{ e^y }{ y^2+1 }dy = \int\limits_{\infty}^{\infty}\frac{ e^y }{ y^2+1 }dy \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0diverges. 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
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