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Integral of y-y^2 dy

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

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

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

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

The answer is:

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

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

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