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