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Identical expressions
(one -sqrt(y))/ two
(1 minus square root of (y)) divide by 2
(one minus square root of (y)) divide by two
(1-√(y))/2
1-sqrty/2
(1-sqrt(y)) divide by 2
Similar expressions
(1+sqrt(y))/2

Integral of (1-sqrt(y))/2 dy

The solution

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  1             
  /             
 |              
 |        ___   
 |  1 - \/ y    
 |  --------- dy
 |      2       
 |              
/               
0

$$\int\limits_{0}^{1} \frac{1 - \sqrt{y}}{2}\, dy$$

Integral((1 - sqrt(y))/2, (y, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

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

$- \frac{y^{\frac{3}{2}}}{3} + \frac{y}{2}+ \mathrm{constant}$

The answer is:

$- \frac{y^{\frac{3}{2}}}{3} + \frac{y}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                            
 |       ___               3/2
 | 1 - \/ y           y   y   
 | --------- dy = C + - - ----
 |     2              2    3  
 |                            
/

$$\int \frac{1 - \sqrt{y}}{2}\, dy = C - \frac{y^{\frac{3}{2}}}{3} + \frac{y}{2}$$

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.

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Integral of (1-sqrt(y))/2 dy

Limits of integration:

The graph:

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The solution