Integral of -x+7 dx

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 |  (-x + 7) dx
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6

$$\int\limits_{6}^{x} \left(7 - x\right)\, dx$$

Integral(-x + 7, (x, 6, x))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 7\, dx = 7 x$
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: $- \frac{x^{2}}{2}$
The result is: $- \frac{x^{2}}{2} + 7 x$
Now simplify:

$\frac{x \left(14 - x\right)}{2}$
Add the constant of integration:

$\frac{x \left(14 - x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(14 - x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         2
 |                         x 
 | (-x + 7) dx = C + 7*x - --
 |                         2 
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$$\int \left(7 - x\right)\, dx = C - \frac{x^{2}}{2} + 7 x$$

Simplify

The answer [src]

             2
            x 
-24 + 7*x - --
            2

$$- \frac{x^{2}}{2} + 7 x - 24$$

             2
            x 
-24 + 7*x - --
            2

$$- \frac{x^{2}}{2} + 7 x - 24$$

-24 + 7*x - x^2/2

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