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Solving integrals/ 3*x*y

Integral of 3*x*y dy

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  3*x*y dy
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∫0x23xy dy\int\limits_{0}^{\frac{x}{2}} 3 x y\, dy 
Integral((3*x)*y, (y, 0, x/2))
Detail solution

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

    ∫3xy dy=3x∫y dy\int 3 x y\, dy = 3 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: 3xy22\frac{3 x y^{2}}{2}

  2. Add the constant of integration:

    3xy22+constant\frac{3 x y^{2}}{2}+ \mathrm{constant}

The answer is:

3xy22+constant\frac{3 x y^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    2
 |                3*x*y 
 | 3*x*y dy = C + ------
 |                  2   
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∫3xy dy=C+3xy22\int 3 x y\, dy = C + \frac{3 x y^{2}}{2}
Simplify
The answer [src] 
   3
3*x 
----
 8
3x38\frac{3 x^{3}}{8} 
=
= 
   3
3*x 
----
 8
3x38\frac{3 x^{3}}{8} 
3*x^3/8

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

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