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Solving integrals/ 2/3xy

Integral of 2/3xy dy

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
     3*x        
 3 - ---        
      2         
    /           
   |            
   |    2*x     
   |    ---*y dy
   |     3      
   |            
  /             
  0
∫03−3x22x3y dy\int\limits_{0}^{3 - \frac{3 x}{2}} \frac{2 x}{3} y\, dy 
Integral((2*x/3)*y, (y, 0, 3 - 3*x/2))
Detail solution

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

    ∫2x3y dy=2x∫y dy3\int \frac{2 x}{3} y\, dy = \frac{2 x \int y\, dy}{3}

    1. The integral of yny^{n} is yn+1n+1\frac{y^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫y dy=y22\int y\, dy = \frac{y^{2}}{2}

    So, the result is: xy23\frac{x y^{2}}{3}

  2. Add the constant of integration:

    xy23+constant\frac{x y^{2}}{3}+ \mathrm{constant}

The answer is:

xy23+constant\frac{x y^{2}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                   
 |                   2
 | 2*x            x*y 
 | ---*y dy = C + ----
 |  3              3  
 |                    
/
∫2x3y dy=C+xy23\int \frac{2 x}{3} y\, dy = C + \frac{x y^{2}}{3}
Simplify
The answer [src] 
           2
  /    3*x\ 
x*|3 - ---| 
  \     2 / 
------------
     3
x(3−3x2)23\frac{x \left(3 - \frac{3 x}{2}\right)^{2}}{3} 
=
= 
           2
  /    3*x\ 
x*|3 - ---| 
  \     2 / 
------------
     3
x(3−3x2)23\frac{x \left(3 - \frac{3 x}{2}\right)^{2}}{3} 
x*(3 - 3*x/2)^2/3

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

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