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Solving integrals/ cos(x)-1/2

Integral of cos(x)-1/2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  pi                  
  --                  
  3                   
   /                  
  |                   
  |  (cos(x) - 1/2) dx
  |                   
 /                    
-pi                   
----                  
 3
$$\int\limits_{- \frac{\pi}{3}}^{\frac{\pi}{3}} \left(\cos{\left(x \right)} - \frac{1}{2}\right)\, dx$$ 
Integral(cos(x) - 1/2, (x, -pi/3, pi/3))
Detail solution

  1. Integrate term-by-term:

    1. The integral of cosine is sine:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                         x         
 | (cos(x) - 1/2) dx = C - - + sin(x)
 |                         2         
/
$$\int \left(\cos{\left(x \right)} - \frac{1}{2}\right)\, dx = C - \frac{x}{2} + \sin{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___   pi
\/ 3  - --
        3
$$- \frac{\pi}{3} + \sqrt{3}$$ 
=
= 
  ___   pi
\/ 3  - --
        3
$$- \frac{\pi}{3} + \sqrt{3}$$ 
sqrt(3) - pi/3
Numerical answer [src] 
0.68485325637228
0.68485325637228

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

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