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x^4/4
Solving integrals/ x^4/4

Integral of x^4/4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
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 |   4   
 |  x    
 |  -- dx
 |  4    
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0
∫01x44 dx\int\limits_{0}^{1} \frac{x^{4}}{4}\, dx 
Integral(x^4/4, (x, 0, 1))
Detail solution

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

    ∫x44 dx=∫x4 dx4\int \frac{x^{4}}{4}\, dx = \frac{\int x^{4}\, dx}{4}

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

      ∫x4 dx=x55\int x^{4}\, dx = \frac{x^{5}}{5}

    So, the result is: x520\frac{x^{5}}{20}

  2. Add the constant of integration:

    x520+constant\frac{x^{5}}{20}+ \mathrm{constant}

The answer is:

x520+constant\frac{x^{5}}{20}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /              
 |               
 |  4           5
 | x           x 
 | -- dx = C + --
 | 4           20
 |               
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∫x44 dx=C+x520\int \frac{x^{4}}{4}\, dx = C + \frac{x^{5}}{20}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.000.50
Plot the graph f(x)
The answer [src] 
1/20
120\frac{1}{20} 
=
= 
1/20
120\frac{1}{20} 
1/20
Numerical answer [src] 
0.05
0.05
The graph
Integral of x^4/4 dx

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

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