Sr Examen
Integral de (1-x)*sin((pi*n*x)) dx
Solución
Ha introducido
[src]
2 / | | (1 - x)*sin(pi*n*x) dx | / 1
$$\int\limits_{1}^{2} \left(1 - x\right) \sin{\left(x \pi n \right)}\, dx$$
Integral((1 - x)*sin((pi*n)*x), (x, 1, 2))
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
/ // 0 for n = 0\ || //sin(pi*n*x) \ | // 0 for n = 0\
| || | || ||----------- for pi*n != 0| | || |
| (1 - x)*sin(pi*n*x) dx = C - x*|<-cos(pi*n*x) | + |<-|< pi*n | | + |<-cos(pi*n*x) |
| ||------------- otherwise| || || | | ||------------- otherwise|
/ \\ pi*n / || \\ x otherwise / | \\ pi*n /
||------------------------------- otherwise|
\\ pi*n /
$$\int \left(1 - x\right) \sin{\left(x \pi n \right)}\, dx = C - x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right) + \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\x & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases} + \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/cos(2*pi*n) sin(pi*n) sin(2*pi*n) |----------- + --------- - ----------- for And(n > -oo, n < oo, n != 0) | pi*n 2 2 2 2 < pi *n pi *n | | 0 otherwise \
$$\begin{cases} \frac{\cos{\left(2 \pi n \right)}}{\pi n} + \frac{\sin{\left(\pi n \right)}}{\pi^{2} n^{2}} - \frac{\sin{\left(2 \pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/cos(2*pi*n) sin(pi*n) sin(2*pi*n) |----------- + --------- - ----------- for And(n > -oo, n < oo, n != 0) | pi*n 2 2 2 2 < pi *n pi *n | | 0 otherwise \
$$\begin{cases} \frac{\cos{\left(2 \pi n \right)}}{\pi n} + \frac{\sin{\left(\pi n \right)}}{\pi^{2} n^{2}} - \frac{\sin{\left(2 \pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((cos(2*pi*n)/(pi*n) + sin(pi*n)/(pi^2*n^2) - sin(2*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.