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Solving integrals/ 2*x*y-(x^2/2)

Integral of 2*x*y-(x^2/2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  /         2\   
 |  |        x |   
 |  |2*x*y - --| dy
 |  \        2 /   
 |                 
/                  
0
$$\int\limits_{0}^{1} \left(- \frac{x^{2}}{2} + 2 x y\right)\, dy$$ 
Integral((2*x)*y - x^2/2, (y, 0, 1))
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*x 
 | |2*x*y - --| dy = C + x*y  - ----
 | \        2 /                  2  
 |                                  
/
$$\int \left(- \frac{x^{2}}{2} + 2 x y\right)\, dy = C - \frac{x^{2} y}{2} + x y^{2}$$
Simplify
The answer [src] 
     2
    x 
x - --
    2
$$- \frac{x^{2}}{2} + x$$ 
=
= 
     2
    x 
x - --
    2
$$- \frac{x^{2}}{2} + x$$ 
x - x^2/2

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

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