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1/2x^2-2x+5

Integral of 1/2x^2-2x+5 dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |  / 2          \   
 |  |x           |   
 |  |-- - 2*x + 5| dx
 |  \2           /   
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \left(\frac{x^{2}}{2} - 2 x + 5\right)\, dx$$
Detail solution
  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 a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      So, 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
 | |x           |           2         x 
 | |-- - 2*x + 5| dx = C - x  + 5*x + --
 | \2           /                     6 
 |                                      
/                                       
$${{x^3}\over{6}}-x^2+5\,x$$
The graph
The answer [src]
25/6
$${{25}\over{6}}$$
=
=
25/6
$$\frac{25}{6}$$
Numerical answer [src]
4.16666666666667
4.16666666666667
The graph
Integral of 1/2x^2-2x+5 dx

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