Integral of (x-1)dx dx

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

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

Detail solution

Let $u = x - 1$ .

Then let $du = dx$ and substitute $du$ :

$\int u\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u\, du = \frac{u^{2}}{2}$
Now substitute $u$ back in:

$\frac{\left(x - 1\right)^{2}}{2}$
Now simplify:

$\frac{\left(x - 1\right)^{2}}{2}$
Add the constant of integration:

$\frac{\left(x - 1\right)^{2}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\left(x - 1\right)^{2}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          2
 |                    (x - 1) 
 | (x - 1)*1 dx = C + --------
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$${{x^2}\over{2}}-x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2

$$-{{1}\over{2}}$$

-1/2

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

Simplify

Numerical answer [src]

-0.5

-0.5

The graph

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