Integral of y-x dx

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                  2      
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 | (y - x) dx = C - -- + x*y
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\int \left(- x + y\right)\, dx = C - \frac{x^{2}}{2} + x y

Simplify

The answer [src]

-1/2 + y

y - \frac{1}{2}

-1/2 + y

y - \frac{1}{2}

-1/2 + y

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