Integral of x^2-6x dx

The solution

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  6              
  /              
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 |  / 2      \   
 |  \x  - 6*x/ dx
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/                
0

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

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

Detail solution

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

$\frac{x^{2} \left(x - 9\right)}{3}$
Add the constant of integration:

$\frac{x^{2} \left(x - 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x - 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-36

$$-36$$

-36

$$-36$$

-36

Numerical answer [src]

-36.0

-36.0

The graph

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

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Integral of x^2-6x dx

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The solution