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