Integral of 1/sqrt(y) dy

The solution

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

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

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

Detail solution

Let $u = \sqrt{y}$ .

Then let $du = \frac{dy}{2 \sqrt{y}}$ and substitute $2 du$ :

$\int 2\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  So, the result is: $2 u$
Now substitute $u$ back in:

$2 \sqrt{y}$
Add the constant of integration:

$2 \sqrt{y}+ \mathrm{constant}$

The answer is:

$2 \sqrt{y}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$2$$

Numerical answer [src]

1.99999999946942

1.99999999946942

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 1/sqrt(y) dy

Limits of integration:

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Piecewise:

The solution