Sr Examen
Integral de 2/pi*(7*x+1)*sin(nx) dx
Solución
Ha introducido
[src]
pi / | | 2 | --*(7*x + 1)*sin(n*x) dx | pi | / 0
$$\int\limits_{0}^{\pi} \frac{2}{\pi} \left(7 x + 1\right) \sin{\left(n x \right)}\, dx$$
Integral(((2/pi)*(7*x + 1))*sin(n*x), (x, 0, pi))
Respuesta (Indefinida)
[src]
// 0 for n = 0\
|| |
|| //sin(n*x) \ | // 0 for n = 0\ // 0 for n = 0\
|| ||-------- for n != 0| | || | || |
- 14*|<-|< n | | + 2*|<-cos(n*x) | + 14*x*|<-cos(n*x) |
|| || | | ||---------- otherwise| ||---------- otherwise|
/ || \\ x otherwise / | \\ n / \\ n /
| ||------------------------- otherwise|
| 2 \\ n /
| --*(7*x + 1)*sin(n*x) dx = C + ---------------------------------------------------------------------------------------------------------
| pi pi
|
/
$$\int \frac{2}{\pi} \left(7 x + 1\right) \sin{\left(n x \right)}\, dx = C + \frac{14 x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) - 14 \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\begin{cases} \frac{\sin{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\x & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right) + 2 \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{\cos{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right)}{\pi}$$
Respuesta
[src]
/ / cos(pi*n) 7*sin(pi*n) 7*pi*cos(pi*n)\ | 2*|- --------- + ----------- - --------------| | | n 2 n | | 2 \ n / <---- + ---------------------------------------------- for And(n > -oo, n < oo, n != 0) |pi*n pi | | 0 otherwise \
$$\begin{cases} \frac{2 \left(- \frac{7 \pi \cos{\left(\pi n \right)}}{n} - \frac{\cos{\left(\pi n \right)}}{n} + \frac{7 \sin{\left(\pi n \right)}}{n^{2}}\right)}{\pi} + \frac{2}{\pi n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/ / cos(pi*n) 7*sin(pi*n) 7*pi*cos(pi*n)\ | 2*|- --------- + ----------- - --------------| | | n 2 n | | 2 \ n / <---- + ---------------------------------------------- for And(n > -oo, n < oo, n != 0) |pi*n pi | | 0 otherwise \
$$\begin{cases} \frac{2 \left(- \frac{7 \pi \cos{\left(\pi n \right)}}{n} - \frac{\cos{\left(\pi n \right)}}{n} + \frac{7 \sin{\left(\pi n \right)}}{n^{2}}\right)}{\pi} + \frac{2}{\pi n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((2/(pi*n) + 2*(-cos(pi*n)/n + 7*sin(pi*n)/n^2 - 7*pi*cos(pi*n)/n)/pi, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.