Sr Examen
Integral de exp(-(x-9.18)^2/(2*0.94))/(sqrt(2*pi)*0.94) dx
Solución
Ha introducido
[src]
oo / | | 2 | / 459\ | -|x - ---| | \ 50/ | ------------ | /47*2\ | |----| | \ 50 / | e | ------------- dx | / ______ \ | |\/ 2*pi *47| | |-----------| | \ 50 / | / 47/5
$$\int\limits_{\frac{47}{5}}^{\infty} \frac{e^{\frac{\left(-1\right) \left(x - \frac{459}{50}\right)^{2}}{\frac{47}{50} \cdot 2}}}{\frac{47}{50} \sqrt{2 \pi}}\, dx$$
Integral(exp((-(x - 459/50)^2)/((47*2/50)))/((sqrt(2*pi)*47/50)), (x, 47/5, oo))
Respuesta (Indefinida)
[src]
/ | | 2 | / 459\ | -|x - ---| | \ 50/ / ____ / 459 \\ | ------------ ___ |5*\/ 47 *|- --- + x|| | /47*2\ ____ ____ 25*\/ 2 | \ 50 /| | |----| \/ 47 *\/ pi *---------*erf|--------------------| | \ 50 / ____ \ 47 / | e 47*\/ pi | ------------- dx = C + ------------------------------------------------- | / ______ \ 10 | |\/ 2*pi *47| | |-----------| | \ 50 / | /
$$\int \frac{e^{\frac{\left(-1\right) \left(x - \frac{459}{50}\right)^{2}}{\frac{47}{50} \cdot 2}}}{\frac{47}{50} \sqrt{2 \pi}}\, dx = C + \frac{\sqrt{47} \sqrt{\pi} \frac{25 \sqrt{2}}{47 \sqrt{\pi}} \operatorname{erf}{\left(\frac{5 \sqrt{47} \left(x - \frac{459}{50}\right)}{47} \right)}}{10}$$
Gráfica
Respuesta
[src]
/ / ____\\
| ____ ____ |11*\/ 47 ||
| ____ ____ 10*\/ 47 *\/ pi *erf|---------||
___ |10*\/ 47 *\/ pi \ 470 /|
11*\/ 2 *|---------------- - -------------------------------|
\ 11 11 /
-------------------------------------------------------------
____
188*\/ pi
$$\frac{11 \sqrt{2} \left(- \frac{10 \sqrt{47} \sqrt{\pi} \operatorname{erf}{\left(\frac{11 \sqrt{47}}{470} \right)}}{11} + \frac{10 \sqrt{47} \sqrt{\pi}}{11}\right)}{188 \sqrt{\pi}}$$
=
=
/ / ____\\
| ____ ____ |11*\/ 47 ||
| ____ ____ 10*\/ 47 *\/ pi *erf|---------||
___ |10*\/ 47 *\/ pi \ 470 /|
11*\/ 2 *|---------------- - -------------------------------|
\ 11 11 /
-------------------------------------------------------------
____
188*\/ pi
$$\frac{11 \sqrt{2} \left(- \frac{10 \sqrt{47} \sqrt{\pi} \operatorname{erf}{\left(\frac{11 \sqrt{47}}{470} \right)}}{11} + \frac{10 \sqrt{47} \sqrt{\pi}}{11}\right)}{188 \sqrt{\pi}}$$
11*sqrt(2)*(10*sqrt(47)*sqrt(pi)/11 - 10*sqrt(47)*sqrt(pi)*erf(11*sqrt(47)/470)/11)/(188*sqrt(pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.