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Solving integrals/ x^2*(x-1)dx

Integral of x^2*(x-1)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Rewrite the integrand:

  2. 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:

  3. Now simplify:

  4. Add the constant of integration:

The answer is:

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

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