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Integral of d{x}:
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Graphing y =:
-x^2-3x-2
Canonical form:
-x^2-3x-2
Identical expressions
-x^ two -3x- two
minus x squared minus 3x minus 2
minus x to the power of two minus 3x minus two
-x2-3x-2
-x²-3x-2
-x to the power of 2-3x-2
-x^2-3x-2dx
Similar expressions
-x^2-3x+2
-x^2+3x-2
x^2-3x-2

Solving integrals/ -x^2-3x-2

Integral of -x^2-3x-2 dx

The solution

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

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

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

Detail solution

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

$\frac{x \left(- 2 x^{2} - 9 x - 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} - 9 x - 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} - 9 x - 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/6

$$\frac{1}{6}$$

1/6

$$\frac{1}{6}$$

Упростить

Numerical answer [src]

0.166666666666667

0.166666666666667

The graph

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

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Identical expressions

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Integral of -x^2-3x-2 dx

Limits of integration:

The graph:

Piecewise:

The solution