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Resolución de integrales/ sqrt((7(1-sinx))^2+(-7cosx)^2)

Integral de sqrt((7(1-sinx))^2+(-7cosx)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  pi                                         
  --                                         
  6                                          
   /                                         
  |                                          
  |     __________________________________   
  |    /                 2              2    
  |  \/  (7*(1 - sin(x)))  + (-7*cos(x))   dx
  |                                          
 /                                           
-pi                                          
----                                         
 6
∫−π6π6(7(1−sin⁡(x)))2+(−7cos⁡(x))2 dx\int\limits_{- \frac{\pi}{6}}^{\frac{\pi}{6}} \sqrt{\left(7 \left(1 - \sin{\left(x \right)}\right)\right)^{2} + \left(- 7 \cos{\left(x \right)}\right)^{2}}\, dx 
Integral(sqrt((7*(1 - sin(x)))^2 + (-7*cos(x))^2), (x, -pi/6, pi/6))
Respuesta (Indefinida) [src] 
  /                                                   /                                        
 |                                                   |                                         
 |    __________________________________             |    __________________________________   
 |   /                 2              2              |   /        2         2                  
 | \/  (7*(1 - sin(x)))  + (-7*cos(x))   dx = C + 7* | \/  1 + cos (x) + sin (x) - 2*sin(x)  dx
 |                                                   |                                         
/                                                   /
∫(7(1−sin⁡(x)))2+(−7cos⁡(x))2 dx=C+7∫sin⁡2(x)−2sin⁡(x)+cos⁡2(x)+1 dx\int \sqrt{\left(7 \left(1 - \sin{\left(x \right)}\right)\right)^{2} + \left(- 7 \cos{\left(x \right)}\right)^{2}}\, dx = C + 7 \int \sqrt{\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} + \cos^{2}{\left(x \right)} + 1}\, dx
Simplificar
Respuesta [src] 
    pi                                         
    --                                         
    6                                          
     /                                         
    |                                          
    |     __________________________________   
    |    /        2         2                  
7*  |  \/  1 + cos (x) + sin (x) - 2*sin(x)  dx
    |                                          
   /                                           
  -pi                                          
  ----                                         
   6
7∫−π6π6sin⁡2(x)−2sin⁡(x)+cos⁡2(x)+1 dx7 \int\limits_{- \frac{\pi}{6}}^{\frac{\pi}{6}} \sqrt{\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} + \cos^{2}{\left(x \right)} + 1}\, dx 
=
= 
    pi                                         
    --                                         
    6                                          
     /                                         
    |                                          
    |     __________________________________   
    |    /        2         2                  
7*  |  \/  1 + cos (x) + sin (x) - 2*sin(x)  dx
    |                                          
   /                                           
  -pi                                          
  ----                                         
   6
7∫−π6π6sin⁡2(x)−2sin⁡(x)+cos⁡2(x)+1 dx7 \int\limits_{- \frac{\pi}{6}}^{\frac{\pi}{6}} \sqrt{\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} + \cos^{2}{\left(x \right)} + 1}\, dx 
7*Integral(sqrt(1 + cos(x)^2 + sin(x)^2 - 2*sin(x)), (x, -pi/6, pi/6))
Respuesta numérica [src] 
10.2487113059643
10.2487113059643

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

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