Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2/sqrt(1+x^2)
Integral of 1/√(1-4x^2)
Integral of sin^3x/cosx
Integral of 3*exp(-3*x)
Identical expressions
√((one -cosx)/ two)
√((1 minus co sinus of e of x) divide by 2)
√((one minus co sinus of e of x) divide by two)
√1-cosx/2
√((1-cosx) divide by 2)
√((1-cosx)/2)dx
Similar expressions
√((1+cosx)/2)

Integral of √((1-cosx)/2) dx

The solution

You have entered [src]

 2*POST_GRBEK_SMALL_pi                   
           /                             
          |                              
          |               ____________   
          |              / 1 - cos(x)    
          |             /  ----------  dx
          |           \/       2         
          |                              
         /                               
         0

$$\int\limits_{0}^{2 POST_{GRBEK SMALL \pi}} \sqrt{\frac{1 - \cos{\left(x \right)}}{2}}\, dx$$

Integral(sqrt(1 - cos(x)/2), (x, 0, 2*POST_GRBEK_SMALL_pi))

Detail solution

Rewrite the integrand:

$\text{True}$
The integral of a constant times a function is the constant times the integral of the function:

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

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

The answer is:

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

The answer (Indefinite) [src]

                                     /                 
                                    |                  
  /                            ___  |   ____________   
 |                           \/ 2 * | \/ 1 - cos(x)  dx
 |     ____________                 |                  
 |    / 1 - cos(x)                 /                   
 |   /  ----------  dx = C + --------------------------
 | \/       2                            2             
 |                                                     
/

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

Simplify

The answer [src]

       2*POST_GRBEK_SMALL_pi                 
                 /                           
                |                            
  ___           |             ____________   
\/ 2 *          |           \/ 1 - cos(x)  dx
                |                            
               /                             
               0                             
---------------------------------------------
                      2

$$\frac{\sqrt{2} \int\limits_{0}^{2 POST_{GRBEK SMALL \pi}} \sqrt{1 - \cos{\left(x \right)}}\, dx}{2}$$

       2*POST_GRBEK_SMALL_pi                 
                 /                           
                |                            
  ___           |             ____________   
\/ 2 *          |           \/ 1 - cos(x)  dx
                |                            
               /                             
               0                             
---------------------------------------------
                      2

$$\frac{\sqrt{2} \int\limits_{0}^{2 POST_{GRBEK SMALL \pi}} \sqrt{1 - \cos{\left(x \right)}}\, dx}{2}$$

Упростить

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of √((1-cosx)/2) dx

Limits of integration:

The graph:

Piecewise:

The solution