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Resolución de integrales/ cos(x/4)/ sin(x/4)/ sin(x/4)^6cos(x/4)^2

Integral de sin(x/4)^6cos(x/4)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |     6/x\    2/x\   
 |  sin |-|*cos |-| dx
 |      \4/     \4/   
 |                    
/                     
0
$$\int\limits_{0}^{1} \sin^{6}{\left(\frac{x}{4} \right)} \cos^{2}{\left(\frac{x}{4} \right)}\, dx$$ 
Integral(sin(x/4)^6*cos(x/4)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                  7/x\    /x\        /x\    /x\        3/x\    /x\      5/x\    /x\
 |                                sin |-|*cos|-|   5*cos|-|*sin|-|   5*sin |-|*cos|-|   sin |-|*cos|-|
 |    6/x\    2/x\          5*x       \4/    \4/        \4/    \4/         \4/    \4/       \4/    \4/
 | sin |-|*cos |-| dx = C + --- + -------------- - --------------- - ---------------- - --------------
 |     \4/     \4/          128         2                 32                48                12      
 |                                                                                                    
/
$$\int \sin^{6}{\left(\frac{x}{4} \right)} \cos^{2}{\left(\frac{x}{4} \right)}\, dx = C + \frac{5 x}{128} + \frac{\sin^{7}{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}}{2} - \frac{\sin^{5}{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}}{12} - \frac{5 \sin^{3}{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}}{48} - \frac{5 \sin{\left(\frac{x}{4} \right)} \cos{\left(\frac{x}{4} \right)}}{32}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
         7                                            3                    5              
 5    sin (1/4)*cos(1/4)   5*cos(1/4)*sin(1/4)   5*sin (1/4)*cos(1/4)   sin (1/4)*cos(1/4)
--- + ------------------ - ------------------- - -------------------- - ------------------
128           2                     32                    48                    12
$$- \frac{5 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{32} - \frac{5 \sin^{3}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{48} - \frac{\sin^{5}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{12} + \frac{\sin^{7}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{2} + \frac{5}{128}$$ 
=
= 
         7                                            3                    5              
 5    sin (1/4)*cos(1/4)   5*cos(1/4)*sin(1/4)   5*sin (1/4)*cos(1/4)   sin (1/4)*cos(1/4)
--- + ------------------ - ------------------- - -------------------- - ------------------
128           2                     32                    48                    12
$$- \frac{5 \sin{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{32} - \frac{5 \sin^{3}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{48} - \frac{\sin^{5}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{12} + \frac{\sin^{7}{\left(\frac{1}{4} \right)} \cos{\left(\frac{1}{4} \right)}}{2} + \frac{5}{128}$$ 
5/128 + sin(1/4)^7*cos(1/4)/2 - 5*cos(1/4)*sin(1/4)/32 - 5*sin(1/4)^3*cos(1/4)/48 - sin(1/4)^5*cos(1/4)/12
Respuesta numérica [src] 
3.16380427038615e-5
3.16380427038615e-5

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

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