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Integral of x-1/2 dx

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
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
 | (x - 1/2) dx = C + -- - -
 |                    2    2
/

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

Simplify

The answer [src]

 2    
x    x
-- - -
2    2

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

 2    
x    x
-- - -
2    2

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

Упростить

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