Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^(-2)
Integral of sin(3x)
Integral of logx
Integral of x^2/(1+x)
Identical expressions
x/ two -x^ three / two
x divide by 2 minus x cubed divide by 2
x divide by two minus x to the power of three divide by two
x/2-x3/2
x/2-x³/2
x/2-x to the power of 3/2
x divide by 2-x^3 divide by 2
x/2-x^3/2dx
Similar expressions
x/2+x^3/2

Integral of x/2-x^3/2 dx

The solution

You have entered [src]

  1            
  /            
 |             
 |  /     3\   
 |  |x   x |   
 |  |- - --| dx
 |  \2   2 /   
 |             
/              
0

$$\int\limits_{0}^{1} \left(- \frac{x^{3}}{2} + \frac{x}{2}\right)\, dx$$

Integral(x/2 - x^3/2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{x^{3}}{2}\right)\, dx = - \frac{\int x^{3}\, dx}{2}$
  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: $- \frac{x^{4}}{8}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x}{2}\, dx = \frac{\int x\, dx}{2}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2}}{4}$
The result is: $- \frac{x^{4}}{8} + \frac{x^{2}}{4}$
Now simplify:

$\frac{x^{2} \left(2 - x^{2}\right)}{8}$
Add the constant of integration:

$\frac{x^{2} \left(2 - x^{2}\right)}{8}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 - x^{2}\right)}{8}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 | /     3\           4    2
 | |x   x |          x    x 
 | |- - --| dx = C - -- + --
 | \2   2 /          8    4 
 |                          
/

$$\int \left(- \frac{x^{3}}{2} + \frac{x}{2}\right)\, dx = C - \frac{x^{4}}{8} + \frac{x^{2}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/8

$$\frac{1}{8}$$

1/8

$$\frac{1}{8}$$

1/8

Numerical answer [src]

0.125

0.125

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x/2-x^3/2 dx

Limits of integration:

The graph:

Piecewise:

The solution