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