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Derivative of:
3x^2-9x+6
Identical expressions
3x^ two -9x+ six
3x squared minus 9x plus 6
3x to the power of two minus 9x plus six
3x2-9x+6
3x²-9x+6
3x to the power of 2-9x+6
3x^2-9x+6dx
Similar expressions
3x^2+9x+6
3x^2-9x-6

Solving integrals/ 3x^2-9x+6

Integral of 3x^2-9x+6 dx

The solution

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  2                    
  /                    
 |                     
 |  /   2          \   
 |  \3*x  - 9*x + 6/ dx
 |                     
/                      
-2

$$\int\limits_{-2}^{2} \left(3 x^{2} - 9 x + 6\right)\, dx$$

Integral(3*x^2 - 9*x + 6, (x, -2, 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:
  
  $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $x^{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 9 x\right)\, dx = - \int 9 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 9 x\, dx = 9 \int x\, dx$
    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: $\frac{9 x^{2}}{2}$
  So, the result is: $- \frac{9 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6\, dx = 6 x$
The result is: $x^{3} - \frac{9 x^{2}}{2} + 6 x$
Now simplify:

$\frac{x \left(2 x^{2} - 9 x + 12\right)}{2}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 9 x + 12\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 9 x + 12\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         2
 | /   2          \           3         9*x 
 | \3*x  - 9*x + 6/ dx = C + x  + 6*x - ----
 |                                       2  
/

$$x^3-{{9\,x^2}\over{2}}+6\,x$$

Simplify

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Plot the graph f(x)

The answer [src]

$$40$$

Упростить

Numerical answer [src]

40.0

40.0

The graph

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

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Integral of 3x^2-9x+6 dx

Limits of integration:

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Piecewise:

The solution