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Resolución de integrales/ cos(x)/ sin(3x)/ (sin(3x))^2(cos(x))^2

Integral de (sin(3x))^2(cos(x))^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
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 |     2         2      
 |  sin (3*x)*cos (x) dx
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0
$$\int\limits_{0}^{1} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral(sin(3*x)^2*cos(x)^2, (x, 0, 1))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2       2         2       2         2       2         2       2            2                       2                         2                         2                 
cos (1)*cos (3)   cos (1)*sin (3)   cos (3)*sin (1)   sin (1)*sin (3)   17*cos (1)*cos(3)*sin(3)   sin (1)*cos(3)*sin(3)   7*sin (3)*cos(1)*sin(1)   9*cos (3)*cos(1)*sin(1)
--------------- + --------------- + --------------- + --------------- - ------------------------ + --------------------- + ----------------------- + -----------------------
       4                 4                 4                 4                     96                        96                       32                        32
$$\frac{\sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{96} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{7 \sin{\left(1 \right)} \sin^{2}{\left(3 \right)} \cos{\left(1 \right)}}{32} + \frac{\sin^{2}{\left(1 \right)} \sin^{2}{\left(3 \right)}}{4} - \frac{17 \sin{\left(3 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{96} + \frac{\cos^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{9 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{2}{\left(3 \right)}}{32} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4}$$ 
=
= 
   2       2         2       2         2       2         2       2            2                       2                         2                         2                 
cos (1)*cos (3)   cos (1)*sin (3)   cos (3)*sin (1)   sin (1)*sin (3)   17*cos (1)*cos(3)*sin(3)   sin (1)*cos(3)*sin(3)   7*sin (3)*cos(1)*sin(1)   9*cos (3)*cos(1)*sin(1)
--------------- + --------------- + --------------- + --------------- - ------------------------ + --------------------- + ----------------------- + -----------------------
       4                 4                 4                 4                     96                        96                       32                        32
$$\frac{\sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{96} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{7 \sin{\left(1 \right)} \sin^{2}{\left(3 \right)} \cos{\left(1 \right)}}{32} + \frac{\sin^{2}{\left(1 \right)} \sin^{2}{\left(3 \right)}}{4} - \frac{17 \sin{\left(3 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{96} + \frac{\cos^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{9 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{2}{\left(3 \right)}}{32} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4}$$ 
cos(1)^2*cos(3)^2/4 + cos(1)^2*sin(3)^2/4 + cos(3)^2*sin(1)^2/4 + sin(1)^2*sin(3)^2/4 - 17*cos(1)^2*cos(3)*sin(3)/96 + sin(1)^2*cos(3)*sin(3)/96 + 7*sin(3)^2*cos(1)*sin(1)/32 + 9*cos(3)^2*cos(1)*sin(1)/32
Respuesta numérica [src] 
0.383495846153048
0.383495846153048

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

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