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Resolución de integrales/ sen(x)/ sen(3x)/ sen(2x)/ sen(x)sen(2x)sen(3x)

Integral de sen(x)sen(2x)sen(3x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
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 |  sin(x)*sin(2*x)*sin(3*x) dx
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0
$$\int\limits_{0}^{1} \sin{\left(x \right)} \sin{\left(2 x \right)} \sin{\left(3 x \right)}\, dx$$ 
Integral((sin(x)*sin(2*x))*sin(3*x), (x, 0, 1))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
  3*cos(3)*sin(1)*sin(2)   cos(1)*cos(2)*sin(3)   cos(1)*cos(3)*sin(2)   cos(2)*cos(3)*sin(1)   sin(1)*sin(2)*sin(3)   cos(2)*sin(1)*sin(3)   cos(1)*sin(2)*sin(3)
- ---------------------- - -------------------- + -------------------- + -------------------- + -------------------- + -------------------- + --------------------
            8                       4                      4                      4                      4                      6                      24
$$\frac{\sin{\left(2 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(2 \right)}}{6} + \frac{\sin{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{24} - \frac{\sin{\left(3 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{4} + \frac{\sin{\left(1 \right)} \sin{\left(2 \right)} \sin{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)} \cos{\left(2 \right)} \cos{\left(3 \right)}}{4} - \frac{3 \sin{\left(1 \right)} \sin{\left(2 \right)} \cos{\left(3 \right)}}{8}$$ 
=
= 
  3*cos(3)*sin(1)*sin(2)   cos(1)*cos(2)*sin(3)   cos(1)*cos(3)*sin(2)   cos(2)*cos(3)*sin(1)   sin(1)*sin(2)*sin(3)   cos(2)*sin(1)*sin(3)   cos(1)*sin(2)*sin(3)
- ---------------------- - -------------------- + -------------------- + -------------------- + -------------------- + -------------------- + --------------------
            8                       4                      4                      4                      4                      6                      24
$$\frac{\sin{\left(2 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(2 \right)}}{6} + \frac{\sin{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{24} - \frac{\sin{\left(3 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{4} + \frac{\sin{\left(1 \right)} \sin{\left(2 \right)} \sin{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)} \cos{\left(2 \right)} \cos{\left(3 \right)}}{4} - \frac{3 \sin{\left(1 \right)} \sin{\left(2 \right)} \cos{\left(3 \right)}}{8}$$ 
-3*cos(3)*sin(1)*sin(2)/8 - cos(1)*cos(2)*sin(3)/4 + cos(1)*cos(3)*sin(2)/4 + cos(2)*cos(3)*sin(1)/4 + sin(1)*sin(2)*sin(3)/4 + cos(2)*sin(1)*sin(3)/6 + cos(1)*sin(2)*sin(3)/24
Respuesta numérica [src] 
0.2787115094828
0.2787115094828

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

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