Mister Exam

Integral of 2x-2y dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 4 - y              
   /                
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  |   (2*x - 2*y) dx
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 /                  
 1                  
$$\int\limits_{1}^{4 - y} \left(2 x - 2 y\right)\, dx$$
Integral(2*x - 2*y, (x, 1, 4 - y))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                               
 |                       2        
 | (2*x - 2*y) dx = C + x  - 2*x*y
 |                                
/                                 
$$\int \left(2 x - 2 y\right)\, dx = C + x^{2} - 2 x y$$
The answer [src]
            2                    
-1 + (4 - y)  + 2*y - 2*y*(4 - y)
$$- 2 y \left(4 - y\right) + 2 y + \left(4 - y\right)^{2} - 1$$
=
=
            2                    
-1 + (4 - y)  + 2*y - 2*y*(4 - y)
$$- 2 y \left(4 - y\right) + 2 y + \left(4 - y\right)^{2} - 1$$
-1 + (4 - y)^2 + 2*y - 2*y*(4 - y)

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