Sr Examen
Integral de (2/(pi*n))*sin((pi*n*x)/2)*4 dx
Solución
Ha introducido
[src]
2 / | | 2 /pi*n*x\ | ----*sin|------|*4 dx | pi*n \ 2 / | / 0
$$\int\limits_{0}^{2} 4 \frac{2}{\pi n} \sin{\left(\frac{x \pi n}{2} \right)}\, dx$$
Integral(((2/((pi*n)))*sin(((pi*n)*x)/2))*4, (x, 0, 2))
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
|| /pi*n*x\ |
8*|<-2*cos|------| |
/ || \ 2 / |
| ||-------------- otherwise|
| 2 /pi*n*x\ \\ pi*n /
| ----*sin|------|*4 dx = C + ------------------------------
| pi*n \ 2 / pi*n
|
/
$$\int 4 \frac{2}{\pi n} \sin{\left(\frac{x \pi n}{2} \right)}\, dx = C + \frac{8 \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{2 \cos{\left(\frac{x \pi n}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{\pi n}$$
Respuesta
[src]
/ 16 16*cos(pi*n) |------ - ------------ for And(n > -oo, n < oo, n != 0) | 2 2 2 2
$$\begin{cases} - \frac{16 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{16}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ 16 16*cos(pi*n) |------ - ------------ for And(n > -oo, n < oo, n != 0) | 2 2 2 2
$$\begin{cases} - \frac{16 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{16}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((16/(pi^2*n^2) - 16*cos(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.