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

The solution

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 |  (x - 1)*(x - 2) dx
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$$\int\limits_{2}^{1} \left(x - 2\right) \left(x - 1\right)\, dx$$

Integral((x - 1)*(x - 2), (x, 2, 1))

Detail solution

Rewrite the integrand:

$\left(x - 2\right) \left(x - 1\right) = x^{2} - 3 x + 2$
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:
  
  $\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$
  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: $- \frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2\, dx = 2 x$
The result is: $\frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x$
Now simplify:

$\frac{x \left(2 x^{2} - 9 x + 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 9 x + 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 9 x + 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  2    3
 |                                3*x    x 
 | (x - 1)*(x - 2) dx = C + 2*x - ---- + --
 |                                 2     3 
/

$$\int \left(x - 2\right) \left(x - 1\right)\, dx = C + \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/6

$$\frac{1}{6}$$

1/6

$$\frac{1}{6}$$

1/6

Numerical answer [src]

0.166666666666667

0.166666666666667

The graph

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

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

Limits of integration:

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The solution