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