Sr Examen
Integral de (4-2*x)cos(n*x) dx
Solución
Ha introducido
[src]
pi / | | (4 - 2*x)*cos(n*x) dx | / 0
$$\int\limits_{0}^{\pi} \left(4 - 2 x\right) \cos{\left(n x \right)}\, dx$$
Integral((4 - 2*x)*cos(n*x), (x, 0, pi))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ || | // x for n = 0\ // x for n = 0\
| ||/-cos(n*x) | || | || |
| (4 - 2*x)*cos(n*x) dx = C + 2*|<|---------- for n != 0 | + 4*|
$$\int \left(4 - 2 x\right) \cos{\left(n x \right)}\, dx = C - 2 x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) + 4 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) + 2 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
/2 2*cos(pi*n) 4*sin(pi*n) 2*pi*sin(pi*n) |-- - ----------- + ----------- - -------------- for And(n > -oo, n < oo, n != 0) | 2 2 n n
$$\begin{cases} - \frac{2 \pi \sin{\left(\pi n \right)}}{n} + \frac{4 \sin{\left(\pi n \right)}}{n} - \frac{2 \cos{\left(\pi n \right)}}{n^{2}} + \frac{2}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \pi^{2} + 4 \pi & \text{otherwise} \end{cases}$$
=
=
/2 2*cos(pi*n) 4*sin(pi*n) 2*pi*sin(pi*n) |-- - ----------- + ----------- - -------------- for And(n > -oo, n < oo, n != 0) | 2 2 n n
$$\begin{cases} - \frac{2 \pi \sin{\left(\pi n \right)}}{n} + \frac{4 \sin{\left(\pi n \right)}}{n} - \frac{2 \cos{\left(\pi n \right)}}{n^{2}} + \frac{2}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- \pi^{2} + 4 \pi & \text{otherwise} \end{cases}$$
Piecewise((2/n^2 - 2*cos(pi*n)/n^2 + 4*sin(pi*n)/n - 2*pi*sin(pi*n)/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-pi^2 + 4*pi, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.