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Identical expressions
(six -3x)/ six
(6 minus 3x) divide by 6
(six minus 3x) divide by six
6-3x/6
(6-3x) divide by 6
(6-3x)/6dx
Similar expressions
(6+3x)/6

Integral of (6-3x)/6 dx

The solution

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  1           
  /           
 |            
 |  6 - 3*x   
 |  ------- dx
 |     6      
 |            
/             
0

$$\int\limits_{0}^{1} \frac{6 - 3 x}{6}\, dx$$

Integral((6 - 3*x)/6, (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{6 - 3 x}{6}\, dx = \frac{\int \left(6 - 3 x\right)\, dx}{6}$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 6\, dx = 6 x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$
    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: $- \frac{3 x^{2}}{2}$
  The result is: $- \frac{3 x^{2}}{2} + 6 x$
So, the result is: $- \frac{x^{2}}{4} + x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                       
 |                       2
 | 6 - 3*x              x 
 | ------- dx = C + x - --
 |    6                 4 
 |                        
/

$$\int \frac{6 - 3 x}{6}\, dx = C - \frac{x^{2}}{4} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/4

$$\frac{3}{4}$$

3/4

$$\frac{3}{4}$$

3/4

Numerical answer [src]

0.75

0.75

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

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Integral of (6-3x)/6 dx

Limits of integration:

The graph:

Piecewise:

The solution