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Integral of d{x}:
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Integral of sqrt(2*x-x^2)/x
Identical expressions
y^(- one / two)
y to the power of ( minus 1 divide by 2)
y to the power of ( minus one divide by two)
y(-1/2)
y-1/2
y^-1/2
y^(-1 divide by 2)
Similar expressions
y^(1/2)

Solving integrals/ y^(-1/2)

Integral of y^(-1/2) dx

The solution

You have entered [src]

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

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

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

Detail solution

The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :

$\int \frac{1}{\sqrt{y}}\, dy = 2 \sqrt{y}$
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 y^(-1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution