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