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Identical expressions
(x/ six)-(seven -x)
(x divide by 6) minus (7 minus x)
(x divide by six) minus (seven minus x)
x/6-7-x
(x divide by 6)-(7-x)
(x/6)-(7-x)dx
Similar expressions
(x/6)-(7+x)
(x/6)+(7-x)

Integral of (x/6)-(7-x) dx

The solution

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  6                
  /                
 |                 
 |  /x         \   
 |  |- + -7 + x| dx
 |  \6         /   
 |                 
/                  
1

$$\int\limits_{1}^{6} \left(\frac{x}{6} + \left(x - 7\right)\right)\, dx$$

Integral(x/6 - 7 + x, (x, 1, 6))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x}{6}\, dx = \frac{\int x\, dx}{6}$
  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: $\frac{x^{2}}{12}$
1. 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:
    
    $\int \left(-7\right)\, dx = - 7 x$
  The result is: $\frac{x^{2}}{2} - 7 x$
The result is: $\frac{7 x^{2}}{12} - 7 x$
Now simplify:

$\frac{7 x \left(x - 12\right)}{12}$
Add the constant of integration:

$\frac{7 x \left(x - 12\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{7 x \left(x - 12\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                                2
 | /x         \                7*x 
 | |- + -7 + x| dx = C - 7*x + ----
 | \6         /                 12 
 |                                 
/

$$\int \left(\frac{x}{6} + \left(x - 7\right)\right)\, dx = C + \frac{7 x^{2}}{12} - 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-175 
-----
  12

$$- \frac{175}{12}$$

-175 
-----
  12

$$- \frac{175}{12}$$

-175/12

Numerical answer [src]

-14.5833333333333

-14.5833333333333

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

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Integral of (x/6)-(7-x) dx

Limits of integration:

The graph:

Piecewise:

The solution