Sr Examen
Integral de xcos(nπx/90) dx
Solución
Ha introducido
[src]
30 / | | /n*pi*x\ | x*cos|------| dx | \ 90 / | / 0
$$\int\limits_{0}^{30} x \cos{\left(\frac{x \pi n}{90} \right)}\, dx$$
Integral(x*cos(((n*pi)*x)/90), (x, 0, 30))
Respuesta (Indefinida)
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// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ || | // x for n = 0\
| || // /pi*n*x\ \ | || |
| /n*pi*x\ || ||-90*cos|------| | | || /pi*n*x\ |
| x*cos|------| dx = C - |< || \ 90 / pi*n | | + x*|<90*sin|------| |
| \ 90 / ||90*|<--------------- for ---- != 0| | || \ 90 / |
| || || pi*n 90 | | ||-------------- otherwise|
/ || || | | \\ pi*n /
|| \\ 0 otherwise / |
||------------------------------------ otherwise|
|| pi*n |
\\ /
$$\int x \cos{\left(\frac{x \pi n}{90} \right)}\, dx = C + x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{90 \sin{\left(\frac{\pi n x}{90} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{90 \left(\begin{cases} - \frac{90 \cos{\left(\frac{\pi n x}{90} \right)}}{\pi n} & \text{for}\: \frac{\pi n}{90} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ /pi*n\ /pi*n\ | 2700*sin|----| 8100*cos|----| | 8100 \ 3 / \ 3 / |- ------ + -------------- + -------------- for And(n > -oo, n < oo, n != 0) < 2 2 pi*n 2 2 | pi *n pi *n | | 450 otherwise \
$$\begin{cases} \frac{2700 \sin{\left(\frac{\pi n}{3} \right)}}{\pi n} + \frac{8100 \cos{\left(\frac{\pi n}{3} \right)}}{\pi^{2} n^{2}} - \frac{8100}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\450 & \text{otherwise} \end{cases}$$
=
=
/ /pi*n\ /pi*n\ | 2700*sin|----| 8100*cos|----| | 8100 \ 3 / \ 3 / |- ------ + -------------- + -------------- for And(n > -oo, n < oo, n != 0) < 2 2 pi*n 2 2 | pi *n pi *n | | 450 otherwise \
$$\begin{cases} \frac{2700 \sin{\left(\frac{\pi n}{3} \right)}}{\pi n} + \frac{8100 \cos{\left(\frac{\pi n}{3} \right)}}{\pi^{2} n^{2}} - \frac{8100}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\450 & \text{otherwise} \end{cases}$$
Piecewise((-8100/(pi^2*n^2) + 2700*sin(pi*n/3)/(pi*n) + 8100*cos(pi*n/3)/(pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (450, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.