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Solving integrals/ y=x^2-x

Integral of y=x^2-x dx

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 |  \x  - x/ dx
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0

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

Integral(x^2 - x, (x, 0, 2))

Detail solution

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: $\frac{x^{3}}{3} - \frac{x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x - 3\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(2 x - 3\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x - 3\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

2/3

$$\frac{2}{3}$$

2/3

$$\frac{2}{3}$$

2/3

Numerical answer [src]

0.666666666666667

0.666666666666667

The graph

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