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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                   
  /                   
 |                    
 |  / 3      2    \   
 |  \x  - 2*x  + x/ dx
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \left(x + \left(x^{3} - 2 x^{2}\right)\right)\, dx$$
Integral(x^3 - 2*x^2 + x, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of is when :

    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:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                           2      3    4
 | / 3      2    \          x    2*x    x 
 | \x  - 2*x  + x/ dx = C + -- - ---- + --
 |                          2     3     4 
/                                         
$$\int \left(x + \left(x^{3} - 2 x^{2}\right)\right)\, dx = C + \frac{x^{4}}{4} - \frac{2 x^{3}}{3} + \frac{x^{2}}{2}$$
The graph
The answer [src]
1/12
$$\frac{1}{12}$$
=
=
1/12
$$\frac{1}{12}$$
1/12
Numerical answer [src]
0.0833333333333333
0.0833333333333333

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