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Solving integrals/ y^2-y

Integral of y^2-y dx

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$$\int\limits_{0}^{1} \left(y^{2} - y\right)\, dy$$

Integral(y^2 - y, (y, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                         
 |                    2    3
 | / 2    \          y    y 
 | \y  - y/ dy = C - -- + --
 |                   2    3 
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/6

$$- \frac{1}{6}$$

-1/6

$$- \frac{1}{6}$$

-1/6

Numerical answer [src]

-0.166666666666667

-0.166666666666667

The graph

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