Sr Examen
Integral de (4-x/2)*cos(pi*n*x) dx
Solución
Ha introducido
[src]
1 / | | / x\ | |4 - -|*cos(pi*n*x) dx | \ 2/ | / -1
$$\int\limits_{-1}^{1} \left(- \frac{x}{2} + 4\right) \cos{\left(x \pi n \right)}\, dx$$
Integral((4 - x/2)*cos((pi*n)*x), (x, -1, 1))
Respuesta (Indefinida)
[src]
/ 2
| x
| -- for n = 0
| 2
|
|/-cos(pi*n*x)
<|------------- for pi*n != 0
|< pi*n
|| // x for n = 0\
|\ 0 otherwise || |
/ |----------------------------- otherwise x*|
$$\int \left(- \frac{x}{2} + 4\right) \cos{\left(x \pi n \right)}\, dx = C - \frac{x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{2} + 4 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \frac{\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}}{2}$$
Respuesta
[src]
/8*sin(pi*n) |----------- for And(n > -oo, n < oo, n != 0) < pi*n | \ 8 otherwise
$$\begin{cases} \frac{8 \sin{\left(\pi n \right)}}{\pi n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\8 & \text{otherwise} \end{cases}$$
=
=
/8*sin(pi*n) |----------- for And(n > -oo, n < oo, n != 0) < pi*n | \ 8 otherwise
$$\begin{cases} \frac{8 \sin{\left(\pi n \right)}}{\pi n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\8 & \text{otherwise} \end{cases}$$
Piecewise((8*sin(pi*n)/(pi*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (8, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.