Sr Examen
Integral de xe^(-(x+9)^2/0,5) dx
Solución
Ha introducido
[src]
oo / | | 2 | -(x + 9) | ---------- | 1/2 | x*E dx | / -oo
oo
/
|
| 2
| -(x + 9)
| ----------
| 1/2
| x*E dx
|
/
-oo
Integral(x*E^((-(x + 9)^2)/(1/2)), (x, -oo, oo))
Respuesta
[src]
/ ___ -162\
___ | ____ / / ___\\ \/ 2 *e |
9*\/ 2 *|- 2*\/ pi *\2 - erfc\9*\/ 2 // - -----------| / ___ 162 ___ ____ / ___ -162 ____ / ___\\ 162\ -162
\ 9 / \- 1458*pi*\/ 2 *e + \/ 2 *\/ pi *\81*\/ 2 *e + 1458*\/ pi *erf\9*\/ 2 //*e /*e
------------------------------------------------------ + --------------------------------------------------------------------------------------------
8 ____
648*\/ pi
$$\frac{9 \sqrt{2} \left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(9 \sqrt{2} \right)}\right) - \frac{\sqrt{2}}{9 e^{162}}\right)}{8} + \frac{- 1458 \sqrt{2} \pi e^{162} + \sqrt{2} \sqrt{\pi} \left(\frac{81 \sqrt{2}}{e^{162}} + 1458 \sqrt{\pi} \operatorname{erf}{\left(9 \sqrt{2} \right)}\right) e^{162}}{648 \sqrt{\pi} e^{162}}$$
=
=
/ ___ -162\
___ | ____ / / ___\\ \/ 2 *e |
9*\/ 2 *|- 2*\/ pi *\2 - erfc\9*\/ 2 // - -----------| / ___ 162 ___ ____ / ___ -162 ____ / ___\\ 162\ -162
\ 9 / \- 1458*pi*\/ 2 *e + \/ 2 *\/ pi *\81*\/ 2 *e + 1458*\/ pi *erf\9*\/ 2 //*e /*e
------------------------------------------------------ + --------------------------------------------------------------------------------------------
8 ____
648*\/ pi
$$\frac{9 \sqrt{2} \left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(9 \sqrt{2} \right)}\right) - \frac{\sqrt{2}}{9 e^{162}}\right)}{8} + \frac{- 1458 \sqrt{2} \pi e^{162} + \sqrt{2} \sqrt{\pi} \left(\frac{81 \sqrt{2}}{e^{162}} + 1458 \sqrt{\pi} \operatorname{erf}{\left(9 \sqrt{2} \right)}\right) e^{162}}{648 \sqrt{\pi} e^{162}}$$
9*sqrt(2)*(-2*sqrt(pi)*(2 - erfc(9*sqrt(2))) - sqrt(2)*exp(-162)/9)/8 + (-1458*pi*sqrt(2)*exp(162) + sqrt(2)*sqrt(pi)*(81*sqrt(2)*exp(-162) + 1458*sqrt(pi)*erf(9*sqrt(2)))*exp(162))*exp(-162)/(648*sqrt(pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.