Integral of (2x³-2x²+2x-2)dx dx

The solution

You have entered [src]

  1                           
  /                           
 |                            
 |  /   3      2          \   
 |  \2*x  - 2*x  + 2*x - 2/ dx
 |                            
/                             
0

$$\int\limits_{0}^{1} \left(\left(2 x + \left(2 x^{3} - 2 x^{2}\right)\right) - 2\right)\, dx$$

Integral(2*x^3 - 2*x^2 + 2*x - 2, (x, 0, 1))

Detail solution

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

$\frac{x \left(3 x^{3} - 4 x^{2} + 6 x - 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(3 x^{3} - 4 x^{2} + 6 x - 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{3} - 4 x^{2} + 6 x - 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-7/6

$$- \frac{7}{6}$$

-7/6

$$- \frac{7}{6}$$

-7/6

Numerical answer [src]

-1.16666666666667

-1.16666666666667

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (2x³-2x²+2x-2)dx dx

Limits of integration:

The graph:

Piecewise:

The solution