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Integral de 4x*sin(ax) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |  4*x*sin(a*x) dx
 |                 
/                  
0                  
$$\int\limits_{0}^{1} 4 x \sin{\left(a x \right)}\, dx$$
Integral((4*x)*sin(a*x), (x, 0, 1))
Respuesta (Indefinida) [src]
                           //            0              for a = 0\                               
                           ||                                    |                               
  /                        || //sin(a*x)            \            |       //    0       for a = 0\
 |                         || ||--------  for a != 0|            |       ||                     |
 | 4*x*sin(a*x) dx = C - 4*|<-|<   a                |            | + 4*x*|<-cos(a*x)            |
 |                         || ||                    |            |       ||----------  otherwise|
/                          || \\   x      otherwise /            |       \\    a                /
                           ||-------------------------  otherwise|                               
                           \\            a                       /                               
$$\int 4 x \sin{\left(a x \right)}\, dx = C + 4 x \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos{\left(a x \right)}}{a} & \text{otherwise} \end{cases}\right) - 4 \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\begin{cases} \frac{\sin{\left(a x \right)}}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}}{a} & \text{otherwise} \end{cases}\right)$$
Respuesta [src]
/  4*cos(a)   4*sin(a)                                  
|- -------- + --------  for And(a > -oo, a < oo, a != 0)
|     a           2                                     
<                a                                      
|                                                       
|          0                       otherwise            
\                                                       
$$\begin{cases} - \frac{4 \cos{\left(a \right)}}{a} + \frac{4 \sin{\left(a \right)}}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
=
/  4*cos(a)   4*sin(a)                                  
|- -------- + --------  for And(a > -oo, a < oo, a != 0)
|     a           2                                     
<                a                                      
|                                                       
|          0                       otherwise            
\                                                       
$$\begin{cases} - \frac{4 \cos{\left(a \right)}}{a} + \frac{4 \sin{\left(a \right)}}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((-4*cos(a)/a + 4*sin(a)/a^2, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.