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Integral of sqrt(1+(1-sinx)^2) dx

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The solution

You have entered [src]
 pi                          
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 2                           
  /                          
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 |     ___________________   
 |    /                 2    
 |  \/  1 + (1 - sin(x))   dx
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/                            
0                            
$$\int\limits_{0}^{\frac{\pi}{2}} \sqrt{\left(1 - \sin{\left(x \right)}\right)^{2} + 1}\, dx$$
Integral(sqrt(1 + (1 - sin(x))^2), (x, 0, pi/2))
The answer [src]
 pi                          
 --                          
 2                           
  /                          
 |                           
 |     ___________________   
 |    /                 2    
 |  \/  1 + (1 - sin(x))   dx
 |                           
/                            
0                            
$$\int\limits_{0}^{\frac{\pi}{2}} \sqrt{\left(1 - \sin{\left(x \right)}\right)^{2} + 1}\, dx$$
=
=
 pi                          
 --                          
 2                           
  /                          
 |                           
 |     ___________________   
 |    /                 2    
 |  \/  1 + (1 - sin(x))   dx
 |                           
/                            
0                            
$$\int\limits_{0}^{\frac{\pi}{2}} \sqrt{\left(1 - \sin{\left(x \right)}\right)^{2} + 1}\, dx$$
Integral(sqrt(1 + (1 - sin(x))^2), (x, 0, pi/2))
Numerical answer [src]
1.72943036971057
1.72943036971057

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