Sr Examen
Integral de (-x)*(cos(pi*n*x))/2 dx
Solución
Ha introducido
[src]
2 / | | -x*cos(pi*n*x) | -------------- dx | 2 | / 0
$$\int\limits_{0}^{2} \frac{- x \cos{\left(x \pi n \right)}}{2}\, dx$$
Integral(((-x)*cos((pi*n)*x))/2, (x, 0, 2))
Respuesta (Indefinida)
[src]
/ 2
| x
| -- for n = 0
| 2
|
|/-cos(pi*n*x)
<|------------- for pi*n != 0
|< pi*n
|| // x for n = 0\
|\ 0 otherwise || |
/ |----------------------------- otherwise x*|
$$\int \frac{- x \cos{\left(x \pi n \right)}}{2}\, dx = C - \frac{x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(\pi n x \right)}}{\pi n} & \text{otherwise} \end{cases}\right)}{2} + \frac{\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(\pi n x \right)}}{\pi n} & \text{for}\: \pi n \neq 0 \\0 & \text{otherwise} \end{cases}}{\pi n} & \text{otherwise} \end{cases}}{2}$$
Respuesta
[src]
/ 1 sin(2*pi*n) cos(2*pi*n) |-------- - ----------- - ----------- for And(n > -oo, n < oo, n != 0) | 2 2 pi*n 2 2 <2*pi *n 2*pi *n | | -1 otherwise \
$$\begin{cases} - \frac{\sin{\left(2 \pi n \right)}}{\pi n} - \frac{\cos{\left(2 \pi n \right)}}{2 \pi^{2} n^{2}} + \frac{1}{2 \pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\-1 & \text{otherwise} \end{cases}$$
=
=
/ 1 sin(2*pi*n) cos(2*pi*n) |-------- - ----------- - ----------- for And(n > -oo, n < oo, n != 0) | 2 2 pi*n 2 2 <2*pi *n 2*pi *n | | -1 otherwise \
$$\begin{cases} - \frac{\sin{\left(2 \pi n \right)}}{\pi n} - \frac{\cos{\left(2 \pi n \right)}}{2 \pi^{2} n^{2}} + \frac{1}{2 \pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\-1 & \text{otherwise} \end{cases}$$
Piecewise((1/(2*pi^2*n^2) - sin(2*pi*n)/(pi*n) - cos(2*pi*n)/(2*pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-1, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.