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x^2-x-6

Integral of x^2-x-6 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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  3                
  /                
 |                 
 |  / 2        \   
 |  \x  - x - 6/ dx
 |                 
/                  
-2                 
$$\int\limits_{-2}^{3} \left(\left(x^{2} - x\right) - 6\right)\, dx$$
Integral(x^2 - x - 6, (x, -2, 3))
Detail solution
  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of is when :

      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]
  /                                   
 |                              2    3
 | / 2        \                x    x 
 | \x  - x - 6/ dx = C - 6*x - -- + --
 |                             2    3 
/                                     
$$\int \left(\left(x^{2} - x\right) - 6\right)\, dx = C + \frac{x^{3}}{3} - \frac{x^{2}}{2} - 6 x$$
The graph
The answer [src]
-125/6
$$- \frac{125}{6}$$
=
=
-125/6
$$- \frac{125}{6}$$
-125/6
Numerical answer [src]
-20.8333333333333
-20.8333333333333
The graph
Integral of x^2-x-6 dx

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