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Graphing y =:
4-3x-x^2
Identical expressions
four -3x-x^ two
4 minus 3x minus x squared
four minus 3x minus x to the power of two
4-3x-x2
4-3x-x²
4-3x-x to the power of 2
4-3x-x^2dx
Similar expressions
4+3x-x^2
4-3x+x^2

Integral of 4-3x-x^2 dx

The solution

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  0                  
  /                  
 |                   
 |  /           2\   
 |  \4 - 3*x - x / dx
 |                   
/                    
-4

$$\int\limits_{-4}^{0} \left(- x^{2} + \left(4 - 3 x\right)\right)\, dx$$

Integral(4 - 3*x - x^2, (x, -4, 0))

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

$\frac{x \left(- 2 x^{2} - 9 x + 24\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} - 9 x + 24\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} - 9 x + 24\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

56/3

$$\frac{56}{3}$$

56/3

$$\frac{56}{3}$$

56/3

Numerical answer [src]

18.6666666666667

18.6666666666667

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

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Integral of 4-3x-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution