Sr Examen
Integral de (sin(x)+sin(2x))*(sin(nx)) dx
Solución
Ha introducido
[src]
pi / | | (sin(x) + sin(2*x))*sin(n*x) dx | / 0
$$\int\limits_{0}^{\pi} \left(\sin{\left(x \right)} + \sin{\left(2 x \right)}\right) \sin{\left(n x \right)}\, dx$$
Integral((sin(x) + sin(2*x))*sin(n*x), (x, 0, pi))
Respuesta
[src]
/ -pi | ---- for Or(n = -2, n = -1) | 2 | | pi | -- for Or(n = 1, n = 2) < 2 | | 2 | 2*sin(pi*n) n *sin(pi*n) |------------- + ------------- otherwise | 4 2 4 2 \4 + n - 5*n 4 + n - 5*n
$$\begin{cases} - \frac{\pi}{2} & \text{for}\: n = -2 \vee n = -1 \\\frac{\pi}{2} & \text{for}\: n = 1 \vee n = 2 \\\frac{n^{2} \sin{\left(\pi n \right)}}{n^{4} - 5 n^{2} + 4} + \frac{2 \sin{\left(\pi n \right)}}{n^{4} - 5 n^{2} + 4} & \text{otherwise} \end{cases}$$
=
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/ -pi | ---- for Or(n = -2, n = -1) | 2 | | pi | -- for Or(n = 1, n = 2) < 2 | | 2 | 2*sin(pi*n) n *sin(pi*n) |------------- + ------------- otherwise | 4 2 4 2 \4 + n - 5*n 4 + n - 5*n
$$\begin{cases} - \frac{\pi}{2} & \text{for}\: n = -2 \vee n = -1 \\\frac{\pi}{2} & \text{for}\: n = 1 \vee n = 2 \\\frac{n^{2} \sin{\left(\pi n \right)}}{n^{4} - 5 n^{2} + 4} + \frac{2 \sin{\left(\pi n \right)}}{n^{4} - 5 n^{2} + 4} & \text{otherwise} \end{cases}$$
Piecewise((-pi/2, (n = -2)∨(n = -1)), (pi/2, (n = 1)∨(n = 2)), (2*sin(pi*n)/(4 + n^4 - 5*n^2) + n^2*sin(pi*n)/(4 + n^4 - 5*n^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.