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