Integral of (x-1) dx

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2

$$- \frac{1}{2}$$

-1/2

$$- \frac{1}{2}$$

-1/2

Numerical answer [src]

-0.5

-0.5

The graph

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