Sr Examen

Otras calculadoras

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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |     2         2      
 |  cos (3*x)*sin (x) dx
 |                      
/                       
0
$$\int\limits_{0}^{1} \sin^{2}{\left(x \right)} \cos^{2}{\left(3 x \right)}\, dx$$ 
Integral(cos(3*x)^2*sin(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)   9*sin (3)*cos(1)*sin(1)   7*cos (3)*cos(1)*sin(1)   cos (1)*cos(3)*sin(3)   17*sin (1)*cos(3)*sin(3)
--------------- + --------------- + --------------- + --------------- - ----------------------- - ----------------------- - --------------------- + ------------------------
       4                 4                 4                 4                     32                        32                       96                       96
$$- \frac{7 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{2}{\left(3 \right)}}{32} + \frac{17 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{96} - \frac{9 \sin{\left(1 \right)} \sin^{2}{\left(3 \right)} \cos{\left(1 \right)}}{32} - \frac{\sin{\left(3 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{96} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)} \sin^{2}{\left(3 \right)}}{4} + \frac{\cos^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4}$$ 
=
= 
   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)   9*sin (3)*cos(1)*sin(1)   7*cos (3)*cos(1)*sin(1)   cos (1)*cos(3)*sin(3)   17*sin (1)*cos(3)*sin(3)
--------------- + --------------- + --------------- + --------------- - ----------------------- - ----------------------- - --------------------- + ------------------------
       4                 4                 4                 4                     32                        32                       96                       96
$$- \frac{7 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{2}{\left(3 \right)}}{32} + \frac{17 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{96} - \frac{9 \sin{\left(1 \right)} \sin^{2}{\left(3 \right)} \cos{\left(1 \right)}}{32} - \frac{\sin{\left(3 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{96} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)} \sin^{2}{\left(3 \right)}}{4} + \frac{\cos^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)} \cos^{2}{\left(3 \right)}}{4}$$ 
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 - 9*sin(3)^2*cos(1)*sin(1)/32 - 7*cos(3)^2*cos(1)*sin(1)/32 - cos(1)^2*cos(3)*sin(3)/96 + 17*sin(1)^2*cos(3)*sin(3)/96
Respuesta numérica [src] 
0.132886864596717
0.132886864596717

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

    © Sr Examen