Integral of 7-x dx

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  4           
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 |  (7 - x) dx
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$$\int\limits_{0}^{4} \left(7 - x\right)\, dx$$

Integral(7 - x, (x, 0, 4))

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$20$$

Numerical answer [src]

20.0

20.0

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