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x^3/3

Integral of x^3/3 dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1      
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 |   3   
 |  x    
 |  -- dx
 |  3    
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01x33dx\int\limits_{0}^{1} \frac{x^{3}}{3}\, dx
Integral(x^3/3, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    x33dx=x3dx3\int \frac{x^{3}}{3}\, dx = \frac{\int x^{3}\, dx}{3}

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

      x3dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

    So, the result is: x412\frac{x^{4}}{12}

  2. Add the constant of integration:

    x412+constant\frac{x^{4}}{12}+ \mathrm{constant}


The answer is:

x412+constant\frac{x^{4}}{12}+ \mathrm{constant}

The answer (Indefinite) [src]
  /              
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 |  3           4
 | x           x 
 | -- dx = C + --
 | 3           12
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x33dx=C+x412\int \frac{x^{3}}{3}\, dx = C + \frac{x^{4}}{12}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.5
The answer [src]
1/12
112\frac{1}{12}
=
=
1/12
112\frac{1}{12}
1/12
Numerical answer [src]
0.0833333333333333
0.0833333333333333
The graph
Integral of x^3/3 dx

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