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Derivative of:
x^2-8x+12
Graphing y =:
x^2-8x+12
Identical expressions
x^ two -8x+ twelve
x squared minus 8x plus 12
x to the power of two minus 8x plus twelve
x2-8x+12
x²-8x+12
x to the power of 2-8x+12
x^2-8x+12dx
Similar expressions
x^2-8x-12
x^2+8x+12

Integral of x^2-8x+12 dx

The solution

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  6                   
  /                   
 |                    
 |  / 2           \   
 |  \x  - 8*x + 12/ dx
 |                    
/                     
2

$$\int\limits_{2}^{6} \left(\left(x^{2} - 8 x\right) + 12\right)\, dx$$

Integral(x^2 - 8*x + 12, (x, 2, 6))

Detail solution

Integrate term-by-term:
1. 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:
    
    $\int \left(- 8 x\right)\, dx = - 8 \int x\, dx$
    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: $- 4 x^{2}$
  The result is: $\frac{x^{3}}{3} - 4 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 12\, dx = 12 x$
The result is: $\frac{x^{3}}{3} - 4 x^{2} + 12 x$
Now simplify:

$\frac{x \left(x^{2} - 12 x + 36\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 12 x + 36\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 12 x + 36\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | / 2           \             2          x 
 | \x  - 8*x + 12/ dx = C - 4*x  + 12*x + --
 |                                        3 
/

$$\int \left(\left(x^{2} - 8 x\right) + 12\right)\, dx = C + \frac{x^{3}}{3} - 4 x^{2} + 12 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-32/3

$$- \frac{32}{3}$$

-32/3

$$- \frac{32}{3}$$

-32/3

Numerical answer [src]

-10.6666666666667

-10.6666666666667

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

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Integral of x^2-8x+12 dx

Limits of integration:

The graph:

Piecewise:

The solution