Sr Examen
Integral de y*exp((-7*y^2+14*y-7)/3) dy
Solución
Ha introducido
[src]
oo / | | 2 | - 7*y + 14*y - 7 | ----------------- | 3 | y*e dy | / -oo
$$\int\limits_{-\infty}^{\infty} y e^{\frac{\left(- 7 y^{2} + 14 y\right) - 7}{3}}\, dy$$
Integral(y*exp((-7*y^2 + 14*y - 7)/3), (y, -oo, oo))
Gráfica
Respuesta
[src]
/ / / ____\\ \
| | ____ |\/ 21 || |
/ / / ____\\ ____ -7/3\ | ____ 7/3 | ____ -7/3 7*\/ pi *erf|------|| |
____ | ____ | |\/ 21 || 2*\/ 21 *e | | 7*pi*\/ 21 *e ____ ____ |\/ 21 *e \ 3 /| 7/3| -7/3
\/ 21 *|- 2*\/ pi *|2 - erfc|------|| - --------------| 9*|- ---------------- + \/ 21 *\/ pi *|------------ + --------------------|*e |*e
\ \ \ 3 // 7 / \ 9 \ 9 9 / /
- ------------------------------------------------------- - ---------------------------------------------------------------------------------------
28 ____
98*\/ pi
$$- \frac{9 \left(- \frac{7 \sqrt{21} \pi e^{\frac{7}{3}}}{9} + \sqrt{21} \sqrt{\pi} \left(\frac{\sqrt{21}}{9 e^{\frac{7}{3}}} + \frac{7 \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{21}}{3} \right)}}{9}\right) e^{\frac{7}{3}}\right)}{98 \sqrt{\pi} e^{\frac{7}{3}}} - \frac{\sqrt{21} \left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(\frac{\sqrt{21}}{3} \right)}\right) - \frac{2 \sqrt{21}}{7 e^{\frac{7}{3}}}\right)}{28}$$
=
=
/ / / ____\\ \
| | ____ |\/ 21 || |
/ / / ____\\ ____ -7/3\ | ____ 7/3 | ____ -7/3 7*\/ pi *erf|------|| |
____ | ____ | |\/ 21 || 2*\/ 21 *e | | 7*pi*\/ 21 *e ____ ____ |\/ 21 *e \ 3 /| 7/3| -7/3
\/ 21 *|- 2*\/ pi *|2 - erfc|------|| - --------------| 9*|- ---------------- + \/ 21 *\/ pi *|------------ + --------------------|*e |*e
\ \ \ 3 // 7 / \ 9 \ 9 9 / /
- ------------------------------------------------------- - ---------------------------------------------------------------------------------------
28 ____
98*\/ pi
$$- \frac{9 \left(- \frac{7 \sqrt{21} \pi e^{\frac{7}{3}}}{9} + \sqrt{21} \sqrt{\pi} \left(\frac{\sqrt{21}}{9 e^{\frac{7}{3}}} + \frac{7 \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{21}}{3} \right)}}{9}\right) e^{\frac{7}{3}}\right)}{98 \sqrt{\pi} e^{\frac{7}{3}}} - \frac{\sqrt{21} \left(- 2 \sqrt{\pi} \left(2 - \operatorname{erfc}{\left(\frac{\sqrt{21}}{3} \right)}\right) - \frac{2 \sqrt{21}}{7 e^{\frac{7}{3}}}\right)}{28}$$
-sqrt(21)*(-2*sqrt(pi)*(2 - erfc(sqrt(21)/3)) - 2*sqrt(21)*exp(-7/3)/7)/28 - 9*(-7*pi*sqrt(21)*exp(7/3)/9 + sqrt(21)*sqrt(pi)*(sqrt(21)*exp(-7/3)/9 + 7*sqrt(pi)*erf(sqrt(21)/3)/9)*exp(7/3))*exp(-7/3)/(98*sqrt(pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.