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Integral of -2x^2+8x-6 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                      
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 |  /     2          \   
 |  \- 2*x  + 8*x - 6/ dx
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$$\int\limits_{0}^{1} \left(\left(- 2 x^{2} + 8 x\right) - 6\right)\, dx$$
Integral(-2*x^2 + 8*x - 6, (x, 0, 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   2*x 
 | \- 2*x  + 8*x - 6/ dx = C - 6*x + 4*x  - ----
 |                                           3  
/                                               
$$\int \left(\left(- 2 x^{2} + 8 x\right) - 6\right)\, dx = C - \frac{2 x^{3}}{3} + 4 x^{2} - 6 x$$
The graph
The answer [src]
-8/3
$$- \frac{8}{3}$$
=
=
-8/3
$$- \frac{8}{3}$$
-8/3
Numerical answer [src]
-2.66666666666667
-2.66666666666667

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