Integral of 2x-y dy

The solution

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     ________            
    /      2             
  \/  4 - x              
       /                 
      |                  
      |      (2*x - y) dy
      |                  
     /                   
    ________             
   /      2              
-\/  4 - x

$$\int\limits_{- \sqrt{4 - x^{2}}}^{\sqrt{4 - x^{2}}} \left(2 x - y\right)\, dy$$

Integral(2*x - y, (y, -sqrt(4 - x^2), sqrt(4 - x^2)))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2 x\, dy = 2 x y$
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: $2 x y - \frac{y^{2}}{2}$
Now simplify:

$\frac{y \left(4 x - y\right)}{2}$
Add the constant of integration:

$\frac{y \left(4 x - y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{y \left(4 x - y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

       ________
      /      2 
4*x*\/  4 - x

$$4 x \sqrt{4 - x^{2}}$$

       ________
      /      2 
4*x*\/  4 - x

$$4 x \sqrt{4 - x^{2}}$$

4*x*sqrt(4 - x^2)

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

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Integral of 2x-y dy

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