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Solving integrals/ 4*y-2*y^2

Integral of 4*y-2*y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

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

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

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