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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] 
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∫012sin⁡(x)+2 dx\int\limits_{0}^{1} \sqrt{2 \sin{\left(x \right)} + 2}\, dx
Simplify
Detail solution

  1. Rewrite the integrand:

    2sin⁡(x)+2=2sin⁡(x)+1\sqrt{2 \sin{\left(x \right)} + 2} = \sqrt{2} \sqrt{\sin{\left(x \right)} + 1}

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

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

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

      But the integral is

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

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

  3. Add the constant of integration:

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

The answer is:

2∫sin⁡(x)+1 dx+constant\sqrt{2} \int \sqrt{\sin{\left(x \right)} + 1}\, 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 sin⁡x+2  dx\int {\sqrt{2\,\sin x+2}}{\;dx}
Simplify
The answer [src] 
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      0
∫012 sin⁡x+2  dx\int_{0}^{1}{\sqrt{2\,\sin x+2}\;dx} 
=
= 
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2∫01sin⁡(x)+1 dx\sqrt{2} \int\limits_{0}^{1} \sqrt{\sin{\left(x \right)} + 1}\, dx
Simplify
Numerical answer [src] 
1.70226900017539
1.70226900017539

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

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