Integral of 6-3*x dx

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

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

Detail solution

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: $- \frac{3 x^{2}}{2} + 6 x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-18

$$-18$$

-18

$$-18$$

-18

Numerical answer [src]

-18.0

-18.0

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