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Question Number 143735 by mnjuly1970 last updated on 17/Jun/21

.....Calculus..... Ω:= ∫_(−∞) ^( ∞) (dx/(x^( 2) e^(a/x^2 ) )) =? (a > 0 )

$$ \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{Calculus}..... \\ $$ $$\:\:\:\:\:\:\:\:\Omega:=\:\int_{−\infty} ^{\:\infty} \frac{{dx}}{{x}^{\:\mathrm{2}} \:{e}^{\frac{{a}}{{x}^{\mathrm{2}} }} }\:=?\:\:\left({a}\:>\:\mathrm{0}\:\right) \\ $$

Answered by Dwaipayan Shikari last updated on 17/Jun/21

(1/(x ))=u =2∫_0 ^∞ e^(−au^2 ) du =(√(π/a))

$$\frac{\mathrm{1}}{{x}\:}={u} \\ $$ $$=\mathrm{2}\int_{\mathrm{0}} ^{\infty} {e}^{−{au}^{\mathrm{2}} } {du}\:\:\:\:\:\: \\ $$ $$=\sqrt{\frac{\pi}{{a}}} \\ $$

Commented byDwaipayan Shikari last updated on 17/Jun/21

Sorry sir! I have corrected

$${Sorry}\:{sir}!\:{I}\:{have}\:{corrected} \\ $$

Commented bymnjuly1970 last updated on 17/Jun/21

thanks alot, please recheck..

$$\:{thanks}\:{alot},\:\:{please}\:\:{recheck}.. \\ $$

Commented bymnjuly1970 last updated on 17/Jun/21

thank you so much mr payan.. grateful...

$$\:{thank}\:{you}\:{so}\:{much}\:{mr}\:{payan}.. \\ $$ $${grateful}... \\ $$

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