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