Sr Examen
Integral de (1-(x/2h))*cos(nx) dx
Solución
Ha introducido
[src]
2*h / | | / x \ | |1 - -*h|*cos(n*x) dx | \ 2 / | / 0
$$\int\limits_{0}^{2 h} \left(- h \frac{x}{2} + 1\right) \cos{\left(n x \right)}\, dx$$
Integral((1 - x/2*h)*cos(n*x), (x, 0, 2*h))
Respuesta (Indefinida)
[src]
/ // 2 \ \
| || x | |
| || -- for n = 0| |
| || 2 | |
| || | // x for n = 0\|
| ||/-cos(n*x) | || ||
h*|- |<|---------- for n != 0 | + x*|
$$\int \left(- h \frac{x}{2} + 1\right) \cos{\left(n x \right)}\, dx = C - \frac{h \left(x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{\cos{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right)}{2} + \begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ 2 |sin(2*h*n) h h *sin(2*h*n) h*cos(2*h*n) |---------- + ---- - ------------- - ------------ for And(n > -oo, n < oo, n != 0) | n 2 n 2 < 2*n 2*n | | 3 | - h + 2*h otherwise \
$$\begin{cases} - \frac{h^{2} \sin{\left(2 h n \right)}}{n} - \frac{h \cos{\left(2 h n \right)}}{2 n^{2}} + \frac{h}{2 n^{2}} + \frac{\sin{\left(2 h n \right)}}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- h^{3} + 2 h & \text{otherwise} \end{cases}$$
=
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/ 2 |sin(2*h*n) h h *sin(2*h*n) h*cos(2*h*n) |---------- + ---- - ------------- - ------------ for And(n > -oo, n < oo, n != 0) | n 2 n 2 < 2*n 2*n | | 3 | - h + 2*h otherwise \
$$\begin{cases} - \frac{h^{2} \sin{\left(2 h n \right)}}{n} - \frac{h \cos{\left(2 h n \right)}}{2 n^{2}} + \frac{h}{2 n^{2}} + \frac{\sin{\left(2 h n \right)}}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\- h^{3} + 2 h & \text{otherwise} \end{cases}$$
Piecewise((sin(2*h*n)/n + h/(2*n^2) - h^2*sin(2*h*n)/n - h*cos(2*h*n)/(2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (-h^3 + 2*h, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.