Integral of (x-3)/2 dx

The solution

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  1         
  /         
 |          
 |  x - 3   
 |  ----- dx
 |    2     
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x - 3}{2}\, dx$$

Integral((x - 3)/2, (x, 0, 1))

Detail solution

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

$\int \frac{x - 3}{2}\, dx = \frac{\int \left(x - 3\right)\, dx}{2}$
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:
    
    $\int \left(-3\right)\, dx = - 3 x$
  The result is: $\frac{x^{2}}{2} - 3 x$
So, the result is: $\frac{x^{2}}{4} - \frac{3 x}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-5/4

$$- \frac{5}{4}$$

-5/4

$$- \frac{5}{4}$$

-5/4

Numerical answer [src]

-1.25

-1.25

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

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Integral of (x-3)/2 dx

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The solution