Integral of (x-2)/3 dx

The solution

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  5         
  /         
 |          
 |  x - 2   
 |  ----- dx
 |    3     
 |          
/           
2

$$\int\limits_{2}^{5} \frac{x - 2}{3}\, dx$$

Integral((x - 2)/3, (x, 2, 5))

Detail solution

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

$\int \frac{x - 2}{3}\, dx = \frac{\int \left(x - 2\right)\, dx}{3}$
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:
    
    $\int \left(-2\right)\, dx = - 2 x$
  The result is: $\frac{x^{2}}{2} - 2 x$
So, the result is: $\frac{x^{2}}{6} - \frac{2 x}{3}$
Now simplify:

$\frac{x \left(x - 4\right)}{6}$
Add the constant of integration:

$\frac{x \left(x - 4\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x - 4\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.5

1.5

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

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Integral of (x-2)/3 dx

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The solution