Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*exp(x)
Integral of exp(-x)
Integral of xdx/(sqrt(1-x^2))
Integral of x^3/3
Limit of the function:
x^3/3
Derivative of:
x^3/3
Graphing y =:
x^3/3
Identical expressions
x^ three / three
x cubed divide by 3
x to the power of three divide by three
x3/3
x³/3
x to the power of 3/3
x^3 divide by 3
x^3/3dx
Similar expressions
sin(0.1x)+x^2+(11+x+(x^3)/3-10cos(0.1x))^2
(x^3)/3+(sin5x)/5
(((x^3)/3)-((3x^2)/2)+5)

Solving integrals/ x^3/3

Integral of x^3/3 dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{x^{3}}{3}\, dx$$

Integral(x^3/3, (x, 0, 1))

Detail solution

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

$\int \frac{x^{3}}{3}\, dx = \frac{\int x^{3}\, dx}{3}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
So, the result is: $\frac{x^{4}}{12}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /              
 |               
 |  3           4
 | x           x 
 | -- dx = C + --
 | 3           12
 |               
/

$$\int \frac{x^{3}}{3}\, dx = C + \frac{x^{4}}{12}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/12

$$\frac{1}{12}$$

=

1/12

$$\frac{1}{12}$$

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.