Sr Examen
Integral de (x-1)*sin(pi*n*x) dx
Solución
Ha introducido
[src]
3 / | | (x - 1)*sin(pi*n*x) dx | / 1
$$\int\limits_{1}^{3} \left(x - 1\right) \sin{\left(x \pi n \right)}\, dx$$
Integral((x - 1)*sin((pi*n)*x), (x, 1, 3))
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
/ || //sin(pi*n*x) \ | // 0 for n = 0\ // 0 for n = 0\
| || ||----------- for pi*n != 0| | || | || |
| (x - 1)*sin(pi*n*x) dx = C - |<-|< pi*n | | - |<-cos(pi*n*x) | + x*|<-cos(pi*n*x) |
| || || | | ||------------- otherwise| ||------------- otherwise|
/ || \\ x otherwise / | \\ pi*n / \\ pi*n /
||------------------------------- otherwise|
\\ pi*n /
$$\int \left(x - 1\right) \sin{\left(x \pi n \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\x & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases} - \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/sin(3*pi*n) sin(pi*n) 2*cos(3*pi*n) |----------- - --------- - ------------- for And(n > -oo, n < oo, n != 0) | 2 2 2 2 pi*n < pi *n pi *n | | 0 otherwise \
$$\begin{cases} - \frac{2 \cos{\left(3 \pi n \right)}}{\pi n} - \frac{\sin{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{\sin{\left(3 \pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/sin(3*pi*n) sin(pi*n) 2*cos(3*pi*n) |----------- - --------- - ------------- for And(n > -oo, n < oo, n != 0) | 2 2 2 2 pi*n < pi *n pi *n | | 0 otherwise \
$$\begin{cases} - \frac{2 \cos{\left(3 \pi n \right)}}{\pi n} - \frac{\sin{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{\sin{\left(3 \pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((sin(3*pi*n)/(pi^2*n^2) - sin(pi*n)/(pi^2*n^2) - 2*cos(3*pi*n)/(pi*n), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.