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