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Solving integrals/ (2*x-1/2-x)

Integral of (2*x-1/2-x) dx

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

$$\int\limits_{1}^{3} \left(- x + 2 x - \frac{1}{2}\right)\, dx$$

Integral(2*x - 1*1/2 - x, (x, 1, 3))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  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: $- \frac{x^{2}}{2}$
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:
  
  $\int \left(\left(-1\right) \frac{1}{2}\right)\, dx = - \frac{x}{2}$
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    
 |                          x    x
 | (2*x - 1/2 - x) dx = C + -- - -
 |                          2    2
/

$${{x^2}\over{2}}-{{x}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$3$$

Simplify

Numerical answer [src]

3.0

3.0

The graph

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