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2y^2
Solving integrals/ 2y^2

Integral of 2y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
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 |     2   
 |  2*y  dy
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0
∫012y2 dy\int\limits_{0}^{1} 2 y^{2}\, dy 
Integral(2*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:

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

  2. Add the constant of integration:

    2y33+constant\frac{2 y^{3}}{3}+ \mathrm{constant}

The answer is:

2y33+constant\frac{2 y^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                  3
 |    2          2*y 
 | 2*y  dy = C + ----
 |                3  
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∫2y2 dy=C+2y33\int 2 y^{2}\, dy = C + \frac{2 y^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
2/3
23\frac{2}{3} 
=
= 
2/3
23\frac{2}{3} 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667
The graph
Integral of 2y^2 dx

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

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