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Similar expressions
(1/3x^2+x)

Integral of (1/3x^2-x) dx

The solution

You have entered [src]

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x^{2}}{3}\, dx = \frac{\int x^{2}\, dx}{3}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $\frac{x^{3}}{9}$
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: $\frac{x^{3}}{9} - \frac{x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x - 9\right)}{18}$
Add the constant of integration:

$\frac{x^{2} \left(2 x - 9\right)}{18}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x - 9\right)}{18}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 | / 2    \           2    3
 | |x     |          x    x 
 | |-- - x| dx = C - -- + --
 | \3     /          2    9 
 |                          
/

$$\int \left(\frac{x^{2}}{3} - x\right)\, dx = C + \frac{x^{3}}{9} - \frac{x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

11
--
18

$$\frac{11}{18}$$

11
--
18

$$\frac{11}{18}$$

11/18

Numerical answer [src]

0.611111111111111

0.611111111111111

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

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Identical expressions

Similar expressions

Integral of (1/3x^2-x) dx

Limits of integration:

The graph:

Piecewise:

The solution