Mister Exam

Integral of x³ dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1      
  /      
 |       
 |   3   
 |  x  dx
 |       
/        
0        
01x3dx\int\limits_{0}^{1} x^{3}\, dx
Integral(x^3, (x, 0, 1))
Detail solution
  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}

  2. Add the constant of integration:

    x44+constant\frac{x^{4}}{4}+ \mathrm{constant}


The answer is:

x44+constant\frac{x^{4}}{4}+ \mathrm{constant}

The answer (Indefinite) [src]
  /              
 |              4
 |  3          x 
 | x  dx = C + --
 |             4 
/                
x3dx=C+x44\int x^{3}\, dx = C + \frac{x^{4}}{4}
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
The answer [src]
1/4
14\frac{1}{4}
=
=
1/4
14\frac{1}{4}
1/4
Numerical answer [src]
0.25
0.25
The graph
Integral of x³ dx

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