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Integral of 2xy^2 dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src]
  1          
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 |  2*x*y  dx
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012xy2dx\int\limits_{0}^{1} 2 x y^{2}\, dx
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    2xy2dx=2y2xdx\int 2 x y^{2}\, dx = 2 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: x2y2x^{2} y^{2}

  2. Add the constant of integration:

    x2y2+constantx^{2} y^{2}+ \mathrm{constant}


The answer is:

x2y2+constantx^{2} y^{2}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                     
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 |      2           2  2
 | 2*x*y  dx = C + x *y 
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x2y2x^2\,y^2
The answer [src]
 2
y 
y2y^2
=
=
 2
y 
y2y^{2}

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