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Resolución de integrales/ sin(ax)/ 7x^2*sin(ax)

Integral de 7x^2*sin(ax) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
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 |     2            
 |  7*x *sin(a*x) dx
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0
∫017x2sin⁡(ax) dx\int\limits_{0}^{1} 7 x^{2} \sin{\left(a x \right)}\, dx 
Integral((7*x^2)*sin(a*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                             //                  0                     for a = 0\                                
                             ||                                                 |                                
                             || //cos(a*x)   x*sin(a*x)            \            |                                
  /                          || ||-------- + ----------  for a != 0|            |                                
 |                           || ||    2          a                 |            |        //    0       for a = 0\
 |    2                      || ||   a                             |            |      2 ||                     |
 | 7*x *sin(a*x) dx = C - 14*|<-|<                                 |            | + 7*x *|<-cos(a*x)            |
 |                           || ||          2                      |            |        ||----------  otherwise|
/                            || ||         x                       |            |        \\    a                /
                             || ||         --            otherwise |            |                                
                             || \\         2                       /            |                                
                             ||--------------------------------------  otherwise|                                
                             \\                  a                              /
∫7x2sin⁡(ax) dx=C+7x2({0for a=0−cos⁡(ax)aotherwise)−14({0for a=0−{xsin⁡(ax)a+cos⁡(ax)a2for a≠0x22otherwiseaotherwise)\int 7 x^{2} \sin{\left(a x \right)}\, dx = C + 7 x^{2} \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\cos{\left(a x \right)}}{a} & \text{otherwise} \end{cases}\right) - 14 \left(\begin{cases} 0 & \text{for}\: a = 0 \\- \frac{\begin{cases} \frac{x \sin{\left(a x \right)}}{a} + \frac{\cos{\left(a x \right)}}{a^{2}} & \text{for}\: a \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}}{a} & \text{otherwise} \end{cases}\right)
Simplificar
Respuesta [src] 
/  14   7*cos(a)   14*cos(a)   14*sin(a)                                  
|- -- - -------- + --------- + ---------  for And(a > -oo, a < oo, a != 0)
|   3      a            3           2                                     
<  a                   a           a                                      
|                                                                         
|                   0                                otherwise            
\
{−7cos⁡(a)a+14sin⁡(a)a2+14cos⁡(a)a3−14a3for a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{7 \cos{\left(a \right)}}{a} + \frac{14 \sin{\left(a \right)}}{a^{2}} + \frac{14 \cos{\left(a \right)}}{a^{3}} - \frac{14}{a^{3}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
=
= 
/  14   7*cos(a)   14*cos(a)   14*sin(a)                                  
|- -- - -------- + --------- + ---------  for And(a > -oo, a < oo, a != 0)
|   3      a            3           2                                     
<  a                   a           a                                      
|                                                                         
|                   0                                otherwise            
\
{−7cos⁡(a)a+14sin⁡(a)a2+14cos⁡(a)a3−14a3for a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{7 \cos{\left(a \right)}}{a} + \frac{14 \sin{\left(a \right)}}{a^{2}} + \frac{14 \cos{\left(a \right)}}{a^{3}} - \frac{14}{a^{3}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
Piecewise((-14/a^3 - 7*cos(a)/a + 14*cos(a)/a^3 + 14*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.

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