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