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The double integral of:
4-x-2y
4-x-2y
Identical expressions
four -x-2y
4 minus x minus 2y
four minus x minus 2y
4-x-2ydx
Similar expressions
4-x+2y
4+x-2y

Integral of 4-x-2y dx

The solution

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  1                 
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 |  (4 - x - 2*y) dx
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0

$$\int\limits_{0}^{1} \left(- 2 y + \left(4 - x\right)\right)\, dx$$

Integral(4 - x - 2*y, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(- 2 y\right)\, dx = - 2 x y$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 4\, dx = 4 x$
  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: $- \frac{x^{2}}{2}$
  The result is: $- \frac{x^{2}}{2} + 4 x$
The result is: $- \frac{x^{2}}{2} - 2 x y + 4 x$
Now simplify:

$\frac{x \left(- x - 4 y + 8\right)}{2}$
Add the constant of integration:

$\frac{x \left(- x - 4 y + 8\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x - 4 y + 8\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              2        
 |                              x         
 | (4 - x - 2*y) dx = C + 4*x - -- - 2*x*y
 |                              2         
/

$$\int \left(- 2 y + \left(4 - x\right)\right)\, dx = C - \frac{x^{2}}{2} - 2 x y + 4 x$$

Simplify

The answer [src]

7/2 - 2*y

$$\frac{7}{2} - 2 y$$

7/2 - 2*y

$$\frac{7}{2} - 2 y$$

7/2 - 2*y

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

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Integral of 4-x-2y dx

Limits of integration:

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The solution