Integral of (x-y) dy

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-1

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

Integral(x - y, (y, -1, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                  2      
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 | (x - y) dy = C - -- + x*y
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$$x\,y-{{y^2}\over{2}}$$

Simplify

The answer [src]

2*x

$${{2\,x+1}\over{2}}+{{2\,x-1}\over{2}}$$

2*x

$$2 x$$

Упростить

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