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)
Derivative of:
(x^2-x)/2
Identical expressions
(x^ two -x)/ two
(x squared minus x) divide by 2
(x to the power of two minus x) divide by two
(x2-x)/2
x2-x/2
(x²-x)/2
(x to the power of 2-x)/2
x^2-x/2
(x^2-x) divide by 2
(x^2-x)/2dx
Similar expressions
(x^2+x)/2

Integral of (x^2-x)/2 dx

The solution

You have entered [src]

  2          
  /          
 |           
 |   2       
 |  x  - x   
 |  ------ dx
 |    2      
 |           
/            
1

$$\int\limits_{1}^{2} \frac{x^{2} - x}{2}\, dx$$

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

Detail solution

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

$\int \frac{x^{2} - x}{2}\, dx = \frac{\int \left(x^{2} - x\right)\, dx}{2}$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- x\right)\, dx = - \int x\, dx$
    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: $- \frac{x^{2}}{2}$
  The result is: $\frac{x^{3}}{3} - \frac{x^{2}}{2}$
So, the result is: $\frac{x^{3}}{6} - \frac{x^{2}}{4}$
Now simplify:

$\frac{x^{2} \left(2 x - 3\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \left(2 x - 3\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x - 3\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                        
 |  2               2    3
 | x  - x          x    x 
 | ------ dx = C - -- + --
 |   2             4    6 
 |                        
/

$$\int \frac{x^{2} - x}{2}\, dx = C + \frac{x^{3}}{6} - \frac{x^{2}}{4}$$

Simplify

The graph

Plot the graph f(x)

Numerical answer [src]

0.416666666666667

0.416666666666667

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)/2 dx

Limits of integration:

The graph:

Piecewise:

The solution