Sr Examen
Integral de (x-2)*cos(pi*n*x/6) dx
Solución
Ha introducido
[src]
3 / | | /pi*n*x\ | (x - 2)*cos|------| dx | \ 6 / | / 2
$$\int\limits_{2}^{3} \left(x - 2\right) \cos{\left(\frac{x \pi n}{6} \right)}\, dx$$
Integral((x - 2)*cos(((pi*n)*x)/6), (x, 2, 3))
Respuesta (Indefinida)
[src]
// 2 \
|| x |
|| -- for n = 0|
|| 2 |
/ || | // x for n = 0\ // x for n = 0\
| || // /pi*n*x\ \ | || | || |
| /pi*n*x\ || ||-6*cos|------| | | || /pi*n*x\ | || /pi*n*x\ |
| (x - 2)*cos|------| dx = C - |< || \ 6 / pi*n | | - 2*|<6*sin|------| | + x*|<6*sin|------| |
| \ 6 / ||6*|<-------------- for ---- != 0| | || \ 6 / | || \ 6 / |
| || || pi*n 6 | | ||------------- otherwise| ||------------- otherwise|
/ || || | | \\ pi*n / \\ pi*n /
|| \\ 0 otherwise / |
||---------------------------------- otherwise|
|| pi*n |
\\ /
$$\int \left(x - 2\right) \cos{\left(\frac{x \pi n}{6} \right)}\, dx = C + x \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{6 \sin{\left(\frac{\pi n x}{6} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{6 \sin{\left(\frac{\pi n x}{6} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: n = 0 \\\frac{6 \left(\begin{cases} - \frac{6 \cos{\left(\frac{\pi n x}{6} \right)}}{\pi n} & \text{for}\: \frac{\pi n}{6} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ /pi*n\ /pi*n\ /pi*n\ | 36*cos|----| 6*sin|----| 36*cos|----| | \ 3 / \ 2 / \ 2 / |- ------------ + ----------- + ------------ for And(n > -oo, n < oo, n != 0) < 2 2 pi*n 2 2 | pi *n pi *n | | 1/2 otherwise \
$$\begin{cases} \frac{6 \sin{\left(\frac{\pi n}{2} \right)}}{\pi n} - \frac{36 \cos{\left(\frac{\pi n}{3} \right)}}{\pi^{2} n^{2}} + \frac{36 \cos{\left(\frac{\pi n}{2} \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
=
=
/ /pi*n\ /pi*n\ /pi*n\ | 36*cos|----| 6*sin|----| 36*cos|----| | \ 3 / \ 2 / \ 2 / |- ------------ + ----------- + ------------ for And(n > -oo, n < oo, n != 0) < 2 2 pi*n 2 2 | pi *n pi *n | | 1/2 otherwise \
$$\begin{cases} \frac{6 \sin{\left(\frac{\pi n}{2} \right)}}{\pi n} - \frac{36 \cos{\left(\frac{\pi n}{3} \right)}}{\pi^{2} n^{2}} + \frac{36 \cos{\left(\frac{\pi n}{2} \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
Piecewise((-36*cos(pi*n/3)/(pi^2*n^2) + 6*sin(pi*n/2)/(pi*n) + 36*cos(pi*n/2)/(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.