Question Number 29027 by abdo imad last updated on 03/Feb/18
![find ∫∫_D e^(−y) sin(2xy)dxdy with D=[0,1]×[0,+∞[ then find the value of ∫_0 ^∞ ((sin^2 t)/t) e^(−t) dt .](https://www.tinkutara.com/question/Q29027.png)
$${find}\:\int\int_{{D}} \:{e}^{−{y}} {sin}\left(\mathrm{2}{xy}\right){dxdy}\:{with}\:{D}=\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},+\infty\left[\right.\right. \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}^{\mathrm{2}} {t}}{{t}}\:{e}^{−{t}} {dt}\:\:. \\ $$