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Identical expressions
eight - two x^2
8 minus 2x squared
eight minus two x squared
8-2x2
8-2x²
8-2x to the power of 2
8-2x^2dx
Similar expressions
8+2x^2

Solving integrals/ 8-2x^2

Integral of 8-2x^2 dx

The solution

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  2              
  /              
 |               
 |  /       2\   
 |  \8 - 2*x / dx
 |               
/                
-2

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

Simplify

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$8\,x-{{2\,x^3}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

64/3

$${{64}\over{3}}$$

64/3

$$\frac{64}{3}$$

Simplify

Numerical answer [src]

21.3333333333333

21.3333333333333

The graph

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

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Integral of 8-2x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution