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