Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1÷x
Integral of 7
Integral of x^2*exp(x^3)
Integral of (1+x^2)^1/2
Identical expressions
sqrt(two + two *sin(x))
square root of (2 plus 2 multiply by sinus of (x))
square root of (two plus two multiply by sinus of (x))
√(2+2*sin(x))
sqrt(2+2sin(x))
sqrt2+2sinx
sqrt(2+2*sin(x))dx
Similar expressions
sqrt(2-2*sin(x))
sqrt(2+2*sinx)

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

The solution

You have entered [src]

   0                    
   /                    
  |                     
  |    ______________   
  |  \/ 2 + 2*sin(x)  dx
  |                     
 /                      
-pi                     
----                    
 2

$$\int\limits_{- \frac{\pi}{2}}^{0} \sqrt{2 \sin{\left(x \right)} + 2}\, dx$$

Integral(sqrt(2 + 2*sin(x)), (x, -pi/2, 0))

Detail solution

Rewrite the integrand:

$\sqrt{2 \sin{\left(x \right)} + 2} = \sqrt{2} \sqrt{\sin{\left(x \right)} + 1}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \sqrt{2} \sqrt{\sin{\left(x \right)} + 1}\, dx = \sqrt{2} \int \sqrt{\sin{\left(x \right)} + 1}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int \sqrt{\sin{\left(x \right)} + 1}\, dx$
So, the result is: $\sqrt{2} \int \sqrt{\sin{\left(x \right)} + 1}\, dx$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                  /                 
 |                                  |                  
 |   ______________            ___  |   ____________   
 | \/ 2 + 2*sin(x)  dx = C + \/ 2 * | \/ 1 + sin(x)  dx
 |                                  |                  
/                                  /

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

Simplify

Numerical answer [src]

1.17157287525381

1.17157287525381

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

Other calculators

How to use it?

Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution