Integral of (y-1)dy dx

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  2             
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 |  (y - 1)*1 dy
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1

$$\int\limits_{1}^{2} \left(y - 1\right) 1\, dy$$

Simplify

Detail solution

Let $u = y - 1$ .

Then let $du = dy$ 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:

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                          2
 |                    (y - 1) 
 | (y - 1)*1 dy = C + --------
 |                       2    
/

$${{y^2}\over{2}}-y$$

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.