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sin(x/2)
Solving integrals/ sin(x/2)

Integral of sin(x/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     /x\   
 |  sin|-| dx
 |     \2/   
 |           
/            
0
$$\int\limits_{0}^{1} \sin{\left(\frac{x}{2} \right)}\, dx$$ 
Integral(sin(x/2), (x, 0, 1))
Detail solution

  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 sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                        
 |                         
 |    /x\               /x\
 | sin|-| dx = C - 2*cos|-|
 |    \2/               \2/
 |                         
/
$$\int \sin{\left(\frac{x}{2} \right)}\, dx = C - 2 \cos{\left(\frac{x}{2} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
2 - 2*cos(1/2)
$$2 - 2 \cos{\left(\frac{1}{2} \right)}$$ 
=
= 
2 - 2*cos(1/2)
$$2 - 2 \cos{\left(\frac{1}{2} \right)}$$
Упростить
Numerical answer [src] 
0.244834876219255
0.244834876219255
The graph
Integral of sin(x/2) dx

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

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