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Solving integrals/ 6xy

Integral of 6xy dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  y         
  /         
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 |  6*x*y dy
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/           
0
∫0y6xy dy\int\limits_{0}^{y} 6 x y\, dy
Simplify
Detail solution

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

    ∫6xy dy=6x∫y dy\int 6 x y\, dy = 6 x \int y\, dy

    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: 3xy23 x y^{2}

  2. Add the constant of integration:

    3xy2+constant3 x y^{2}+ \mathrm{constant}

The answer is:

3xy2+constant3 x y^{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                     
 |                     2
 | 6*x*y dy = C + 3*x*y 
 |                      
/
3 x y23\,x\,y^2
Simplify
The answer [src] 
     2
3*x*y
3 x y23\,x\,y^2 
=
= 
     2
3*x*y
3xy23 x y^{2}
Simplify

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

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