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Similar expressions
xdx/2+x^2

Solving integrals/ xdx/2-x^2

Integral of xdx/2-x^2 dx

The solution

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

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

Integral(x/2 - x^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:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  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: $- \frac{x^{3}}{3}$
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: $- \frac{x^{3}}{3} + \frac{x^{2}}{4}$
Now simplify:

$\frac{x^{2} \left(3 - 4 x\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \left(3 - 4 x\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(3 - 4 x\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

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

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

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Identical expressions

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Integral of xdx/2-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution