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