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Integral of -x^2-4x-3 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
 -1                    
  /                    
 |                     
 |  /   2          \   
 |  \- x  - 4*x - 3/ dx
 |                     
/                      
-3                     
$$\int\limits_{-3}^{-1} \left(\left(- x^{2} - 4 x\right) - 3\right)\, dx$$
Integral(-x^2 - 4*x - 3, (x, -3, -1))
Detail solution
  1. 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:

        1. The integral of is when :

        So, the result is:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      The result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                         
 |                                         3
 | /   2          \                   2   x 
 | \- x  - 4*x - 3/ dx = C - 3*x - 2*x  - --
 |                                        3 
/                                           
$$\int \left(\left(- x^{2} - 4 x\right) - 3\right)\, dx = C - \frac{x^{3}}{3} - 2 x^{2} - 3 x$$
The graph
The answer [src]
4/3
$$\frac{4}{3}$$
=
=
4/3
$$\frac{4}{3}$$
4/3
Numerical answer [src]
1.33333333333333
1.33333333333333

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