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Integral of 1/12*(x+2y) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  2           
  /           
 |            
 |  x + 2*y   
 |  ------- dy
 |     12     
 |            
/             
0             
$$\int\limits_{0}^{2} \frac{x + 2 y}{12}\, dy$$
Integral((x + 2*y)/12, (y, 0, 2))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    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:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                         
 |                   2      
 | x + 2*y          y    x*y
 | ------- dy = C + -- + ---
 |    12            12    12
 |                          
/                           
$$\int \frac{x + 2 y}{12}\, dy = C + \frac{x y}{12} + \frac{y^{2}}{12}$$
The answer [src]
1   x
- + -
3   6
$$\frac{x}{6} + \frac{1}{3}$$
=
=
1   x
- + -
3   6
$$\frac{x}{6} + \frac{1}{3}$$
1/3 + x/6

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