Integral of 3x-6 dx

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 |  (3*x - 6) dx
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$$\int\limits_{0}^{2} \left(3 x - 6\right)\, dx$$

Integral(3*x - 6, (x, 0, 2))

Detail solution

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

$\frac{3 x \left(x - 4\right)}{2}$
Add the constant of integration:

$\frac{3 x \left(x - 4\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 x \left(x - 4\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            2
 |                          3*x 
 | (3*x - 6) dx = C - 6*x + ----
 |                           2  
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$$\int \left(3 x - 6\right)\, dx = C + \frac{3 x^{2}}{2} - 6 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-6

$$-6$$

-6

$$-6$$

-6

Numerical answer [src]

-6.0

-6.0

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