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x^2/3
Solving integrals/ x^2/3

Integral of x^2/3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
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 |   2   
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 |  -- dx
 |  3    
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0
∫01x23 dx\int\limits_{0}^{1} \frac{x^{2}}{3}\, dx 
Integral(x^2/3, (x, 0, 1))
Detail solution

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

    ∫x23 dx=∫x2 dx3\int \frac{x^{2}}{3}\, dx = \frac{\int x^{2}\, dx}{3}

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

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    So, the result is: x39\frac{x^{3}}{9}

  2. Add the constant of integration:

    x39+constant\frac{x^{3}}{9}+ \mathrm{constant}

The answer is:

x39+constant\frac{x^{3}}{9}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /              
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 |  2           3
 | x           x 
 | -- dx = C + --
 | 3           9 
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∫x23 dx=C+x39\int \frac{x^{2}}{3}\, dx = C + \frac{x^{3}}{9}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Plot the graph f(x)
The answer [src] 
1/9
19\frac{1}{9} 
=
= 
1/9
19\frac{1}{9} 
1/9
Numerical answer [src] 
0.111111111111111
0.111111111111111
The graph
Integral of x^2/3 dx

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

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