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Integral of sqrt((1-cos(2*x)/2)) dx

Limits of integration:

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The solution

You have entered [src]
 pi                      
 --                      
 2                       
  /                      
 |                       
 |      ______________   
 |     /     cos(2*x)    
 |    /  1 - --------  dx
 |  \/          2        
 |                       
/                        
0                        
$$\int\limits_{0}^{\frac{\pi}{2}} \sqrt{- \frac{\cos{\left(2 x \right)}}{2} + 1}\, dx$$
Integral(sqrt(1 - cos(2*x)/2), (x, 0, pi/2))
The answer (Indefinite) [src]
                                       /                   
                                      |                    
  /                              ___  |   ______________   
 |                             \/ 2 * | \/ 2 - cos(2*x)  dx
 |     ______________                 |                    
 |    /     cos(2*x)                 /                     
 |   /  1 - --------  dx = C + ----------------------------
 | \/          2                            2              
 |                                                         
/                                                          
$$\int \sqrt{- \frac{\cos{\left(2 x \right)}}{2} + 1}\, dx = C + \frac{\sqrt{2} \int \sqrt{2 - \cos{\left(2 x \right)}}\, dx}{2}$$
Numerical answer [src]
1.54463102381839
1.54463102381839

    Use the examples entering the upper and lower limits of integration.