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Integral of 2*x+2*y dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

    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:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

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

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