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Integral of xy^2 dx

Limits of integration:

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Piecewise:

The solution

You have entered [src]
  1        
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 |     2   
 |  x*y  dx
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0          
01xy2dx\int\limits_{0}^{1} x y^{2}\, dx
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    xy2dx=y2xdx\int x y^{2}\, dx = y^{2} \int x\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

      xdx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: x2y22\frac{x^{2} y^{2}}{2}

  2. Add the constant of integration:

    x2y22+constant\frac{x^{2} y^{2}}{2}+ \mathrm{constant}


The answer is:

x2y22+constant\frac{x^{2} y^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                   
 |                2  2
 |    2          x *y 
 | x*y  dx = C + -----
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x2y22{{x^2\,y^2}\over{2}}
The answer [src]
 2
y 
--
2 
y22{{y^2}\over{2}}
=
=
 2
y 
--
2 
y22\frac{y^{2}}{2}

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