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Resolución de integrales/ abs(cos(1/x)/(sin(x))^(2/3))

Integral de abs(cos(1/x)/(sin(x))^(2/3)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |  |     /1\ |   
 |  |  cos|-| |   
 |  |     \x/ |   
 |  |---------| dx
 |  |   2/3   |   
 |  |sin   (x)|   
 |                
/                 
0
∫01∣cos⁡(1x)sin⁡23(x)∣ dx\int\limits_{0}^{1} \left|{\frac{\cos{\left(\frac{1}{x} \right)}}{\sin^{\frac{2}{3}}{\left(x \right)}}}\right|\, dx 
Integral(Abs(cos(1/x)/sin(x)^(2/3)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                       /              
 |                       |               
 | |     /1\ |           |   |   /1\|    
 | |  cos|-| |           |   |cos|-||    
 | |     \x/ |           |   |   \x/|    
 | |---------| dx = C +  | ----------- dx
 | |   2/3   |           | |   2/3   |   
 | |sin   (x)|           | |sin   (x)|   
 |                       |               
/                       /
∫∣cos⁡(1x)sin⁡23(x)∣ dx=C+∫∣cos⁡(1x)∣∣sin⁡23(x)∣ dx\int \left|{\frac{\cos{\left(\frac{1}{x} \right)}}{\sin^{\frac{2}{3}}{\left(x \right)}}}\right|\, dx = C + \int \frac{\left|{\cos{\left(\frac{1}{x} \right)}}\right|}{\left|{\sin^{\frac{2}{3}}{\left(x \right)}}\right|}\, dx
Simplificar
Respuesta [src] 
  1               
  /               
 |                
 |    |   /1\|    
 |    |cos|-||    
 |    |   \x/|    
 |  ----------- dx
 |  |   2/3   |   
 |  |sin   (x)|   
 |                
/                 
0
∫01∣cos⁡(1x)∣∣sin⁡23(x)∣ dx\int\limits_{0}^{1} \frac{\left|{\cos{\left(\frac{1}{x} \right)}}\right|}{\left|{\sin^{\frac{2}{3}}{\left(x \right)}}\right|}\, dx 
=
= 
  1               
  /               
 |                
 |    |   /1\|    
 |    |cos|-||    
 |    |   \x/|    
 |  ----------- dx
 |  |   2/3   |   
 |  |sin   (x)|   
 |                
/                 
0
∫01∣cos⁡(1x)∣∣sin⁡23(x)∣ dx\int\limits_{0}^{1} \frac{\left|{\cos{\left(\frac{1}{x} \right)}}\right|}{\left|{\sin^{\frac{2}{3}}{\left(x \right)}}\right|}\, dx 
Integral(Abs(cos(1/x))/Abs(sin(x)^(2/3)), (x, 0, 1))
Respuesta numérica [src] 
1.74204495976447
1.74204495976447

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

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