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Solving integrals/ cos(x)-1/2

Integral of cos(x)-1/2 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  pi                  
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  3                   
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  |  (cos(x) - 1/2) dx
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-pi                   
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 3
∫−π3π3(cos⁡(x)−12) dx\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:

      ∫cos⁡(x) dx=sin⁡(x)\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}

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

      ∫(−12) dx=−x2\int \left(- \frac{1}{2}\right)\, dx = - \frac{x}{2}

    The result is: −x2+sin⁡(x)- \frac{x}{2} + \sin{\left(x \right)}

  2. Add the constant of integration:

    −x2+sin⁡(x)+constant- \frac{x}{2} + \sin{\left(x \right)}+ \mathrm{constant}

The answer is:

−x2+sin⁡(x)+constant- \frac{x}{2} + \sin{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                  
 |                         x         
 | (cos(x) - 1/2) dx = C - - + sin(x)
 |                         2         
/
∫(cos⁡(x)−12) dx=C−x2+sin⁡(x)\int \left(\cos{\left(x \right)} - \frac{1}{2}\right)\, dx = C - \frac{x}{2} + \sin{\left(x \right)}
Simplify
The graph
-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.0-1.0
Plot the graph f(x)
The answer [src] 
  ___   pi
\/ 3  - --
        3
−π3+3- \frac{\pi}{3} + \sqrt{3} 
=
= 
  ___   pi
\/ 3  - --
        3
−π3+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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