Integral of (2x-1)/2 dx

The solution

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  2           
  /           
 |            
 |  2*x - 1   
 |  ------- dx
 |     2      
 |            
/             
-2

$$\int\limits_{-2}^{2} \frac{2 x - 1}{2}\, dx$$

Integral((2*x - 1)/2, (x, -2, 2))

Detail solution

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

$\int \frac{2 x - 1}{2}\, dx = \frac{\int \left(2 x - 1\right)\, dx}{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x\, dx = 2 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $x^{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-1\right)\, dx = - x$
  The result is: $x^{2} - x$
So, the result is: $\frac{x^{2}}{2} - \frac{x}{2}$
Now simplify:

$\frac{x \left(x - 1\right)}{2}$
Add the constant of integration:

$\frac{x \left(x - 1\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x - 1\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                   2    
 | 2*x - 1          x    x
 | ------- dx = C + -- - -
 |    2             2    2
 |                        
/

$$\int \frac{2 x - 1}{2}\, dx = C + \frac{x^{2}}{2} - \frac{x}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2

$$-2$$

-2

$$-2$$

-2

Numerical answer [src]

-2.0

-2.0

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

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Integral of (2x-1)/2 dx

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The solution