Sr Examen
Integral de -1/3*x*sin(pi*n*x) dx
Solución
Ha introducido
[src]
3 / | | -x | ---*sin(pi*n*x) dx | 3 | / 1
$$\int\limits_{1}^{3} - \frac{x}{3} \sin{\left(x \pi n \right)}\, dx$$
Integral((-x/3)*sin((pi*n)*x), (x, 1, 3))
Respuesta (Indefinida)
[src]
/ 0 for n = 0
|
| //sin(pi*n*x) \
| ||----------- for pi*n != 0|
<-|< pi*n | // 0 for n = 0\
| || | || |
/ | \\ x otherwise / x*|<-cos(pi*n*x) |
| |------------------------------- otherwise ||------------- otherwise|
| -x \ pi*n \\ pi*n /
| ---*sin(pi*n*x) dx = C + ------------------------------------------- - -----------------------------
| 3 3 3
|
/
$$\int - \frac{x}{3} \sin{\left(x \pi n \right)}\, dx = C - \frac{x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{3} + \frac{\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\x & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}}{3}$$
Respuesta
[src]
/cos(3*pi*n) cos(pi*n) sin(3*pi*n) sin(pi*n) |----------- - --------- - ----------- + --------- for And(n > -oo, n < oo, n != 0) | pi*n 3*pi*n 2 2 2 2 < 3*pi *n 3*pi *n | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(\pi n \right)}}{3 \pi n} + \frac{\cos{\left(3 \pi n \right)}}{\pi n} + \frac{\sin{\left(\pi n \right)}}{3 \pi^{2} n^{2}} - \frac{\sin{\left(3 \pi n \right)}}{3 \pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/cos(3*pi*n) cos(pi*n) sin(3*pi*n) sin(pi*n) |----------- - --------- - ----------- + --------- for And(n > -oo, n < oo, n != 0) | pi*n 3*pi*n 2 2 2 2 < 3*pi *n 3*pi *n | | 0 otherwise \
$$\begin{cases} - \frac{\cos{\left(\pi n \right)}}{3 \pi n} + \frac{\cos{\left(3 \pi n \right)}}{\pi n} + \frac{\sin{\left(\pi n \right)}}{3 \pi^{2} n^{2}} - \frac{\sin{\left(3 \pi n \right)}}{3 \pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((cos(3*pi*n)/(pi*n) - cos(pi*n)/(3*pi*n) - sin(3*pi*n)/(3*pi^2*n^2) + sin(pi*n)/(3*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.