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Solving integrals/ sqrt(2-2sinx)

Integral of sqrt(2-2sinx) dx

Limits of integration:

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The solution

You have entered [src] 
 pi                    
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 6                     
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 |  \/ 2 - 2*sin(x)  dx
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∫0π6−2sin⁡(x)+2 dx\int\limits_{0}^{\frac{\pi}{6}} \sqrt{- 2 \sin{\left(x \right)} + 2}\, dx
Simplify
Detail solution

  1. Rewrite the integrand:

    2−2sin⁡(x)=21−sin⁡(x)\sqrt{2 - 2 \sin{\left(x \right)}} = \sqrt{2} \sqrt{1 - \sin{\left(x \right)}}

  2. The integral of a constant times a function is the constant times the integral of the function:

    ∫21−sin⁡(x) dx=2∫1−sin⁡(x) dx\int \sqrt{2} \sqrt{1 - \sin{\left(x \right)}}\, dx = \sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      ∫1−sin⁡(x) dx\int \sqrt{1 - \sin{\left(x \right)}}\, dx

    So, the result is: 2∫1−sin⁡(x) dx\sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx

  3. Add the constant of integration:

    2∫1−sin⁡(x) dx+constant\sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx+ \mathrm{constant}

The answer is:

2∫1−sin⁡(x) dx+constant\sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  /                 
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 |   ______________            ___  |   ____________   
 | \/ 2 - 2*sin(x)  dx = C + \/ 2 * | \/ 1 - sin(x)  dx
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∫2−2 sin⁡x  dx\int {\sqrt{2-2\,\sin x}}{\;dx}
Simplify
The answer [src] 
       pi                  
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       6                   
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  ___  |    ____________   
\/ 2 * |  \/ 1 - sin(x)  dx
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      0
2∫0π6−sin⁡(x)+1 dx\sqrt{2} \int\limits_{0}^{\frac{\pi}{6}} \sqrt{- \sin{\left(x \right)} + 1}\, dx 
=
= 
       pi                  
       --                  
       6                   
        /                  
       |                   
  ___  |    ____________   
\/ 2 * |  \/ 1 - sin(x)  dx
       |                   
      /                    
      0
2∫0π6−sin⁡(x)+1 dx\sqrt{2} \int\limits_{0}^{\frac{\pi}{6}} \sqrt{- \sin{\left(x \right)} + 1}\, dx
Simplify
Numerical answer [src] 
0.635674490391565
0.635674490391565

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

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