Sr Examen
Integral de e^(i*t*x)*f(x) dx
Solución
Ha introducido
[src]
oo / | | I*t*x | E *f*x dx | / 0
$$\int\limits_{0}^{\infty} x e^{x i t} f\, dx$$
Integral((E^((i*t)*x)*f)*x, (x, 0, oo))
Respuesta (Indefinida)
[src]
/// 2\ I*t*x \
||\f*t - I*f*x*t /*e 3 |
/ ||----------------------- for t != 0|
| || 3 |
| I*t*x || t |
| E *f*x dx = C + |< |
| || 2 |
/ || f*x |
|| ---- otherwise |
|| 2 |
\\ /
$$\int x e^{x i t} f\, dx = C + \begin{cases} \frac{\left(- i f t^{2} x + f t\right) e^{i t x}}{t^{3}} & \text{for}\: t^{3} \neq 0 \\\frac{f x^{2}}{2} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ -f | pi | pi | --- for |- -- + arg(t)| < -- | 2 | 2 | 2 | t | | oo < / | | | | I*t*x | | f*x*e dx otherwise | | |/ \0
$$\begin{cases} - \frac{f}{t^{2}} & \text{for}\: \left|{\arg{\left(t \right)} - \frac{\pi}{2}}\right| < \frac{\pi}{2} \\\int\limits_{0}^{\infty} f x e^{i t x}\, dx & \text{otherwise} \end{cases}$$
=
=
/ -f | pi | pi | --- for |- -- + arg(t)| < -- | 2 | 2 | 2 | t | | oo < / | | | | I*t*x | | f*x*e dx otherwise | | |/ \0
$$\begin{cases} - \frac{f}{t^{2}} & \text{for}\: \left|{\arg{\left(t \right)} - \frac{\pi}{2}}\right| < \frac{\pi}{2} \\\int\limits_{0}^{\infty} f x e^{i t x}\, dx & \text{otherwise} \end{cases}$$
Piecewise((-f/t^2, Abs(-pi/2 + arg(t)) < pi/2), (Integral(f*x*exp(i*t*x), (x, 0, oo)), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.