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Solving integrals/ 1/2sin(x)

Integral of 1/2sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi          
 --          
 4           
  /          
 |           
 |  sin(x)   
 |  ------ dx
 |    2      
 |           
/            
pi           
--           
6
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{\sin{\left(x \right)}}{2}\, dx$$ 
Integral(sin(x)/2, (x, pi/6, pi/4))
Detail solution

  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:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                      
 |                       
 | sin(x)          cos(x)
 | ------ dx = C - ------
 |   2               2   
 |                       
/
$$\int \frac{\sin{\left(x \right)}}{2}\, dx = C - \frac{\cos{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    ___     ___
  \/ 2    \/ 3 
- ----- + -----
    4       4
$$- \frac{\sqrt{2}}{4} + \frac{\sqrt{3}}{4}$$ 
=
= 
    ___     ___
  \/ 2    \/ 3 
- ----- + -----
    4       4
$$- \frac{\sqrt{2}}{4} + \frac{\sqrt{3}}{4}$$ 
-sqrt(2)/4 + sqrt(3)/4
Numerical answer [src] 
0.0794593112989455
0.0794593112989455

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

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