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