Sr Examen
Integral de (x+4)*sin(pi*n*x/4) dx
Solución
Ha introducido
[src]
4 / | | /pi*n*x\ | (x + 4)*sin|------| dx | \ 4 / | / 0
$$\int\limits_{0}^{4} \left(x + 4\right) \sin{\left(\frac{x \pi n}{4} \right)}\, dx$$
Integral((x + 4)*sin(((pi*n)*x)/4), (x, 0, 4))
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
/ || // /pi*n*x\ \ | // 0 for n = 0\ // 0 for n = 0\
| || ||4*sin|------| | | || | || |
| /pi*n*x\ || || \ 4 / pi*n | | || /pi*n*x\ | || /pi*n*x\ |
| (x + 4)*sin|------| dx = C - |<-4*|<------------- for ---- != 0| | + 4*|<-4*cos|------| | + x*|<-4*cos|------| |
| \ 4 / || || pi*n 4 | | || \ 4 / | || \ 4 / |
| || || | | ||-------------- otherwise| ||-------------- otherwise|
/ || \\ x otherwise / | \\ pi*n / \\ pi*n /
||---------------------------------- otherwise|
\\ pi*n /
$$\int \left(x + 4\right) \sin{\left(\frac{x \pi n}{4} \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{4 \cos{\left(\frac{\pi n x}{4} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{4 \left(\begin{cases} \frac{4 \sin{\left(\frac{\pi n x}{4} \right)}}{\pi n} & \text{for}\: \frac{\pi n}{4} \neq 0 \\x & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases} + 4 \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{4 \cos{\left(\frac{\pi n x}{4} \right)}}{\pi n} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/ 16 32*cos(pi*n) 16*sin(pi*n) |---- - ------------ + ------------ for And(n > -oo, n < oo, n != 0) |pi*n pi*n 2 2 < pi *n | | 0 otherwise \
$$\begin{cases} - \frac{32 \cos{\left(\pi n \right)}}{\pi n} + \frac{16}{\pi n} + \frac{16 \sin{\left(\pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/ 16 32*cos(pi*n) 16*sin(pi*n) |---- - ------------ + ------------ for And(n > -oo, n < oo, n != 0) |pi*n pi*n 2 2 < pi *n | | 0 otherwise \
$$\begin{cases} - \frac{32 \cos{\left(\pi n \right)}}{\pi n} + \frac{16}{\pi n} + \frac{16 \sin{\left(\pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((16/(pi*n) - 32*cos(pi*n)/(pi*n) + 16*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.