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Solving integrals/ x*(y^2)

Integral of x*(y^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |     2   
 |  x*y  dy
 |         
/          
0
∫01xy2 dy\int\limits_{0}^{1} x y^{2}\, dy 
Integral(x*y^2, (y, 0, 1))
Detail solution

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

    ∫xy2 dy=x∫y2 dy\int x y^{2}\, dy = x \int y^{2}\, dy

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

      ∫y2 dy=y33\int y^{2}\, dy = \frac{y^{3}}{3}

    So, the result is: xy33\frac{x y^{3}}{3}

  2. Add the constant of integration:

    xy33+constant\frac{x y^{3}}{3}+ \mathrm{constant}

The answer is:

xy33+constant\frac{x y^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                  3
 |    2          x*y 
 | x*y  dy = C + ----
 |                3  
/
∫xy2 dy=C+xy33\int x y^{2}\, dy = C + \frac{x y^{3}}{3}
Simplify
The answer [src] 
x
-
3
x3\frac{x}{3} 
=
= 
x
-
3
x3\frac{x}{3} 
x/3

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

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