Sr Examen
Integral de x*exp(-ax)*dx dx
Solución
Ha introducido
[src]
10 / | | -a*x | x*e dx | / 0
$$\int\limits_{0}^{10} x e^{- a x}\, dx$$
Integral(x*exp((-a)*x), (x, 0, 10))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for a = 0|
|| 2 |
/ || | // x for a = 0\
| ||/ -a*x | || |
| -a*x |||e 2 | || -a*x |
| x*e dx = C - |<|----- for a != 0 | + x*|<-e |
| ||| 2 | ||------- otherwise|
/ ||< a otherwise| || a |
||| | \\ /
||| -x |
||| --- otherwise |
||\ a |
\\ /
$$\int x e^{- a x}\, dx = C + x \left(\begin{cases} x & \text{for}\: a = 0 \\- \frac{e^{- a x}}{a} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: a = 0 \\\begin{cases} \frac{e^{- a x}}{a^{2}} & \text{for}\: a^{2} \neq 0 \\- \frac{x}{a} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ -10*a |1 (-1 - 10*a)*e |-- + ------------------ for And(a > -oo, a < oo, a != 0) < 2 2 |a a | \ 50 otherwise
$$\begin{cases} \frac{\left(- 10 a - 1\right) e^{- 10 a}}{a^{2}} + \frac{1}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\50 & \text{otherwise} \end{cases}$$
=
=
/ -10*a |1 (-1 - 10*a)*e |-- + ------------------ for And(a > -oo, a < oo, a != 0) < 2 2 |a a | \ 50 otherwise
$$\begin{cases} \frac{\left(- 10 a - 1\right) e^{- 10 a}}{a^{2}} + \frac{1}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\50 & \text{otherwise} \end{cases}$$
Piecewise((a^(-2) + (-1 - 10*a)*exp(-10*a)/a^2, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (50, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.