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