Integral of x(x-4) dx

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$$\int\limits_{0}^{1} x \left(x - 4\right)\, dx$$

Integral(x*(x - 4), (x, 0, 1))

Detail solution

Rewrite the integrand:

$x \left(x - 4\right) = x^{2} - 4 x$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- 2 x^{2}$
The result is: $\frac{x^{3}}{3} - 2 x^{2}$
Now simplify:

$\frac{x^{2} \left(x - 6\right)}{3}$
Add the constant of integration:

$\frac{x^{2} \left(x - 6\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x - 6\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           3
 |                       2   x 
 | x*(x - 4) dx = C - 2*x  + --
 |                           3 
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$$\int x \left(x - 4\right)\, dx = C + \frac{x^{3}}{3} - 2 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-5/3

$$- \frac{5}{3}$$

-5/3

$$- \frac{5}{3}$$

-5/3

Numerical answer [src]

-1.66666666666667

-1.66666666666667

The graph

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