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Resolución de integrales/ sin^2/ sin^2(4x-7)dx

Integral de sin^2(4x-7)dx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
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 |                  
 |     2            
 |  sin (4*x - 7) dx
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0
$$\int\limits_{0}^{1} \sin^{2}{\left(4 x - 7 \right)}\, dx$$ 
Integral(sin(4*x - 7)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                          
 |                                         3                                                                                                                                           4                                             2                       
 |    2                                 tan (-7/2 + 2*x)                              tan(-7/2 + 2*x)                                     2*x                                   2*x*tan (-7/2 + 2*x)                          4*x*tan (-7/2 + 2*x)           
 | sin (4*x - 7) dx = C + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ------------------------------------------- + -------------------------------------------
 |                                 4                    2                        4                    2                        4                    2                        4                    2                        4                    2            
/                         4 + 4*tan (-7/2 + 2*x) + 8*tan (-7/2 + 2*x)   4 + 4*tan (-7/2 + 2*x) + 8*tan (-7/2 + 2*x)   4 + 4*tan (-7/2 + 2*x) + 8*tan (-7/2 + 2*x)   4 + 4*tan (-7/2 + 2*x) + 8*tan (-7/2 + 2*x)   4 + 4*tan (-7/2 + 2*x) + 8*tan (-7/2 + 2*x)
$$\int \sin^{2}{\left(4 x - 7 \right)}\, dx = C + \frac{2 x \tan^{4}{\left(2 x - \frac{7}{2} \right)}}{4 \tan^{4}{\left(2 x - \frac{7}{2} \right)} + 8 \tan^{2}{\left(2 x - \frac{7}{2} \right)} + 4} + \frac{4 x \tan^{2}{\left(2 x - \frac{7}{2} \right)}}{4 \tan^{4}{\left(2 x - \frac{7}{2} \right)} + 8 \tan^{2}{\left(2 x - \frac{7}{2} \right)} + 4} + \frac{2 x}{4 \tan^{4}{\left(2 x - \frac{7}{2} \right)} + 8 \tan^{2}{\left(2 x - \frac{7}{2} \right)} + 4} + \frac{\tan^{3}{\left(2 x - \frac{7}{2} \right)}}{4 \tan^{4}{\left(2 x - \frac{7}{2} \right)} + 8 \tan^{2}{\left(2 x - \frac{7}{2} \right)} + 4} - \frac{\tan{\left(2 x - \frac{7}{2} \right)}}{4 \tan^{4}{\left(2 x - \frac{7}{2} \right)} + 8 \tan^{2}{\left(2 x - \frac{7}{2} \right)} + 4}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                                   
cos (3)   sin (3)   cos(7)*sin(7)   cos(3)*sin(3)
------- + ------- - ------------- + -------------
   2         2            8               8
$$- \frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{8} + \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{8} + \frac{\sin^{2}{\left(3 \right)}}{2} + \frac{\cos^{2}{\left(3 \right)}}{2}$$ 
=
= 
   2         2                                   
cos (3)   sin (3)   cos(7)*sin(7)   cos(3)*sin(3)
------- + ------- - ------------- + -------------
   2         2            8               8
$$- \frac{\sin{\left(7 \right)} \cos{\left(7 \right)}}{8} + \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{8} + \frac{\sin^{2}{\left(3 \right)}}{2} + \frac{\cos^{2}{\left(3 \right)}}{2}$$ 
cos(3)^2/2 + sin(3)^2/2 - cos(7)*sin(7)/8 + cos(3)*sin(3)/8
Respuesta numérica [src] 
0.420623571631638
0.420623571631638

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

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