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Solving integrals/ sqrt(2-2*sin(x))

Integral of sqrt(2-2*sin(x)) dx

Limits of integration:

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The solution

You have entered [src] 
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∫0π32−2sin⁡(x) dx\int\limits_{0}^{\frac{\pi}{3}} \sqrt{2 - 2 \sin{\left(x \right)}}\, dx 
Integral(sqrt(2 - 2*sin(x)), (x, 0, pi/3))
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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∫2−2sin⁡(x) dx=C+2∫1−sin⁡(x) dx\int \sqrt{2 - 2 \sin{\left(x \right)}}\, dx = C + \sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx
Simplify
Numerical answer [src] 
1.03527618041008
1.03527618041008

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

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