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cos(x/2)/2

Integral of cos(x/2)/2 dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |     /x\   
 |  cos|-|   
 |     \2/   
 |  ------ dx
 |    2      
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{\cos{\left(\frac{x}{2} \right)}}{2}\, dx$$
Integral(cos(x/2)/2, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

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

        1. The integral of cosine is sine:

        So, the result is:

      Now substitute back in:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                      
 |                       
 |    /x\                
 | cos|-|                
 |    \2/             /x\
 | ------ dx = C + sin|-|
 |   2                \2/
 |                       
/                        
$$\int \frac{\cos{\left(\frac{x}{2} \right)}}{2}\, dx = C + \sin{\left(\frac{x}{2} \right)}$$
The graph
The answer [src]
sin(1/2)
$$\sin{\left(\frac{1}{2} \right)}$$
=
=
sin(1/2)
$$\sin{\left(\frac{1}{2} \right)}$$
Numerical answer [src]
0.479425538604203
0.479425538604203
The graph
Integral of cos(x/2)/2 dx

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