Integral of -x-2 dx

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  4            
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 |  (-x - 2) dx
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-2

\int\limits_{-2}^{4} \left(- x - 2\right)\, dx

Integral(-x - 2, (x, -2, 4))

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 is the constant times the variable of integration:
  
  $\int \left(-2\right)\, dx = - 2 x$
The result is: $- \frac{x^{2}}{2} - 2 x$
Now simplify:

$- \frac{x \left(x + 4\right)}{2}$
Add the constant of integration:

$- \frac{x \left(x + 4\right)}{2}+ \mathrm{constant}$

The answer is:

- \frac{x \left(x + 4\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                         2
 |                         x 
 | (-x - 2) dx = C - 2*x - --
 |                         2 
/

\int \left(- x - 2\right)\, dx = C - \frac{x^{2}}{2} - 2 x

Simplify

The graph

Plot the graph f(x)

The answer [src]

-18

-18

-18

-18

-18

Numerical answer [src]

-18.0

-18.0

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