Mister Exam

Other calculators

Solving integrals/ 4*sqrt(2-2sin(x))

Integral of 4*sqrt(2-2sin(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                      
 --                      
 6                       
  /                      
 |                       
 |      ______________   
 |  4*\/ 2 - 2*sin(x)  dx
 |                       
/                        
0
∫0π642−2sin⁡(x) dx\int\limits_{0}^{\frac{\pi}{6}} 4 \sqrt{2 - 2 \sin{\left(x \right)}}\, dx 
Integral(4*sqrt(2 - 2*sin(x)), (x, 0, pi/6))
Detail solution

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

    ∫42−2sin⁡(x) dx=4∫2−2sin⁡(x) dx\int 4 \sqrt{2 - 2 \sin{\left(x \right)}}\, dx = 4 \int \sqrt{2 - 2 \sin{\left(x \right)}}\, dx

    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

    So, the result is: 42∫1−sin⁡(x) dx4 \sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx

  2. Add the constant of integration:

    42∫1−sin⁡(x) dx+constant4 \sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx+ \mathrm{constant}

The answer is:

42∫1−sin⁡(x) dx+constant4 \sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                      /                 
 |                                      |                  
 |     ______________              ___  |   ____________   
 | 4*\/ 2 - 2*sin(x)  dx = C + 4*\/ 2 * | \/ 1 - sin(x)  dx
 |                                      |                  
/                                      /
∫42−2sin⁡(x) dx=C+42∫1−sin⁡(x) dx\int 4 \sqrt{2 - 2 \sin{\left(x \right)}}\, dx = C + 4 \sqrt{2} \int \sqrt{1 - \sin{\left(x \right)}}\, dx
Simplify
Numerical answer [src] 
2.54269796156626
2.54269796156626

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

    © Mister Exam – Calculator