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Resolución de integrales/ sin^2/ (5x-2)/ sin^2(5x-2)

Integral de sin^2(5x-2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     2            
 |  sin (5*x - 2) dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \sin^{2}{\left(5 x - 2 \right)}\, dx$$ 
Integral(sin(5*x - 2)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                         /     5*x\                                   3/     5*x\                                                                                4/     5*x\                                  2/     5*x\            
 |                                     2*tan|-1 + ---|                              2*tan |-1 + ---|                                                                         5*x*tan |-1 + ---|                          10*x*tan |-1 + ---|            
 |    2                                     \      2 /                                    \      2 /                                   5*x                                           \      2 /                                   \      2 /            
 | sin (5*x - 2) dx = C - ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------ + ------------------------------------------
 |                                   4/     5*x\         2/     5*x\              4/     5*x\         2/     5*x\              4/     5*x\         2/     5*x\              4/     5*x\         2/     5*x\              4/     5*x\         2/     5*x\
/                         10 + 10*tan |-1 + ---| + 20*tan |-1 + ---|   10 + 10*tan |-1 + ---| + 20*tan |-1 + ---|   10 + 10*tan |-1 + ---| + 20*tan |-1 + ---|   10 + 10*tan |-1 + ---| + 20*tan |-1 + ---|   10 + 10*tan |-1 + ---| + 20*tan |-1 + ---|
                                      \      2 /          \      2 /               \      2 /          \      2 /               \      2 /          \      2 /               \      2 /          \      2 /               \      2 /          \      2 /
$$\int \sin^{2}{\left(5 x - 2 \right)}\, dx = C + \frac{5 x \tan^{4}{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} + \frac{10 x \tan^{2}{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} + \frac{5 x}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} + \frac{2 \tan^{3}{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10} - \frac{2 \tan{\left(\frac{5 x}{2} - 1 \right)}}{10 \tan^{4}{\left(\frac{5 x}{2} - 1 \right)} + 20 \tan^{2}{\left(\frac{5 x}{2} - 1 \right)} + 10}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                                   
cos (3)   sin (3)   cos(2)*sin(2)   cos(3)*sin(3)
------- + ------- - ------------- - -------------
   2         2            10              10
$$\frac{\sin^{2}{\left(3 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{10} + \frac{\cos^{2}{\left(3 \right)}}{2}$$ 
=
= 
   2         2                                   
cos (3)   sin (3)   cos(2)*sin(2)   cos(3)*sin(3)
------- + ------- - ------------- - -------------
   2         2            10              10
$$\frac{\sin^{2}{\left(3 \right)}}{2} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)}}{10} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{10} + \frac{\cos^{2}{\left(3 \right)}}{2}$$ 
cos(3)^2/2 + sin(3)^2/2 - cos(2)*sin(2)/10 - cos(3)*sin(3)/10
Respuesta numérica [src] 
0.551810899675343
0.551810899675343

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

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