Sr Examen
Integral de exp^(-p*t)*(h/c)*t dt
Solución
Ha introducido
[src]
l / | | -p*t h | E *-*t dt | c | / 0
$$\int\limits_{0}^{l} t e^{- p t} \frac{h}{c}\, dt$$
Integral((E^((-p)*t)*(h/c))*t, (t, 0, l))
Respuesta (Indefinida)
[src]
// -p*t \
||(-h - h*p*t)*e 2 |
/ ||------------------ for c*p != 0|
| || 2 |
| -p*t h || c*p |
| E *-*t dt = C + |< |
| c || 2 |
| || h*t |
/ || ---- otherwise |
|| 2*c |
\\ /
$$\int t e^{- p t} \frac{h}{c}\, dt = C + \begin{cases} \frac{\left(- h p t - h\right) e^{- p t}}{c p^{2}} & \text{for}\: c p^{2} \neq 0 \\\frac{h t^{2}}{2 c} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ -l*p | h (-h - h*l*p)*e 2 |---- + ------------------ for c*p != 0 | 2 2 |c*p c*p < | 2 | h*l | ---- otherwise | 2*c \
$$\begin{cases} \frac{h}{c p^{2}} + \frac{\left(- h l p - h\right) e^{- l p}}{c p^{2}} & \text{for}\: c p^{2} \neq 0 \\\frac{h l^{2}}{2 c} & \text{otherwise} \end{cases}$$
=
=
/ -l*p | h (-h - h*l*p)*e 2 |---- + ------------------ for c*p != 0 | 2 2 |c*p c*p < | 2 | h*l | ---- otherwise | 2*c \
$$\begin{cases} \frac{h}{c p^{2}} + \frac{\left(- h l p - h\right) e^{- l p}}{c p^{2}} & \text{for}\: c p^{2} \neq 0 \\\frac{h l^{2}}{2 c} & \text{otherwise} \end{cases}$$
Piecewise((h/(c*p^2) + (-h - h*l*p)*exp(-l*p)/(c*p^2), Ne(c*p^2, 0)), (h*l^2/(2*c), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.