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x-x^ two + two
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x-x^2+2dx
Similar expressions
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Solving integrals/ x-x^2+2

Integral of x-x^2+2 dx

The solution

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  2                
  /                
 |                 
 |  /     2    \   
 |  \x - x  + 2/ dx
 |                 
/                  
-1

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

Integral(x - x^2 + 2, (x, -1, 2))

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/2

$$\frac{9}{2}$$

9/2

$$\frac{9}{2}$$

9/2

Numerical answer [src]

4.5

4.5

The graph

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

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Integral of x-x^2+2 dx

Limits of integration:

The graph:

Piecewise:

The solution