Sr Examen
Integral de 1/(2*π*√(1-R^2)*exp(-(x^2-2*R*x*y+y^2))/(2*(1-R^2))) dy
Solución
Ha introducido
[src]
1 / | | 1 | --------------------------------------- dy | / ________ 2 2\ | | / 2 - x + 2*r*x*y - y | | |2*pi*\/ 1 - r *e | | |-------------------------------------| | | / 2\ | | \ 2*\1 - r / / | / 0
$$\int\limits_{0}^{1} \frac{1}{\frac{1}{2 \left(1 - r^{2}\right)} 2 \pi \sqrt{1 - r^{2}} e^{- y^{2} + \left(- x^{2} + y 2 r x\right)}}\, dy$$
Integral(1/((((2*pi)*sqrt(1 - r^2))*exp(-x^2 + ((2*r)*x)*y - y^2))/((2*(1 - r^2)))), (y, 0, 1))
Respuesta (Indefinida)
[src]
/ / \
| | |
________ | | / 2\ | / 2\
/ 2 | | \y / -2*r*x*y | \x /
/ \/ 1 - r *| | e *e dy|*e
| | | |
| 1 \/ /
| --------------------------------------- dy = C + -----------------------------------------
| / ________ 2 2\ pi
| | / 2 - x + 2*r*x*y - y |
| |2*pi*\/ 1 - r *e |
| |-------------------------------------|
| | / 2\ |
| \ 2*\1 - r / /
|
/
$$\int \frac{1}{\frac{1}{2 \left(1 - r^{2}\right)} 2 \pi \sqrt{1 - r^{2}} e^{- y^{2} + \left(- x^{2} + y 2 r x\right)}}\, dy = C + \frac{\sqrt{1 - r^{2}} e^{x^{2}} \int e^{y^{2}} e^{- 2 r x y}\, dy}{\pi}$$
Respuesta
[src]
/ 2\ 2 2 / 2\ 2 2
/ 2\ \x / -r *x / 2\ \x / -r *x
\2 - 2*r /*erfi(-1 + r*x)*e *e \2 - 2*r /*erfi(r*x)*e *e
- --------------------------------------- + ----------------------------------
________ ________
____ / 2 ____ / 2
4*\/ pi *\/ 1 - r 4*\/ pi *\/ 1 - r
$$\frac{\left(2 - 2 r^{2}\right) e^{x^{2}} e^{- r^{2} x^{2}} \operatorname{erfi}{\left(r x \right)}}{4 \sqrt{\pi} \sqrt{1 - r^{2}}} - \frac{\left(2 - 2 r^{2}\right) e^{x^{2}} e^{- r^{2} x^{2}} \operatorname{erfi}{\left(r x - 1 \right)}}{4 \sqrt{\pi} \sqrt{1 - r^{2}}}$$
=
=
/ 2\ 2 2 / 2\ 2 2
/ 2\ \x / -r *x / 2\ \x / -r *x
\2 - 2*r /*erfi(-1 + r*x)*e *e \2 - 2*r /*erfi(r*x)*e *e
- --------------------------------------- + ----------------------------------
________ ________
____ / 2 ____ / 2
4*\/ pi *\/ 1 - r 4*\/ pi *\/ 1 - r
$$\frac{\left(2 - 2 r^{2}\right) e^{x^{2}} e^{- r^{2} x^{2}} \operatorname{erfi}{\left(r x \right)}}{4 \sqrt{\pi} \sqrt{1 - r^{2}}} - \frac{\left(2 - 2 r^{2}\right) e^{x^{2}} e^{- r^{2} x^{2}} \operatorname{erfi}{\left(r x - 1 \right)}}{4 \sqrt{\pi} \sqrt{1 - r^{2}}}$$
-(2 - 2*r^2)*erfi(-1 + r*x)*exp(x^2)*exp(-r^2*x^2)/(4*sqrt(pi)*sqrt(1 - r^2)) + (2 - 2*r^2)*erfi(r*x)*exp(x^2)*exp(-r^2*x^2)/(4*sqrt(pi)*sqrt(1 - r^2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.