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1/sqrt(y)
Solving integrals/ 1/sqrt(y)

Integral of 1/sqrt(y) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |    1     
 |  ----- dy
 |    ___   
 |  \/ y    
 |          
/           
0
∫011y dy\int\limits_{0}^{1} \frac{1}{\sqrt{y}}\, dy 
Integral(1/(sqrt(y)), (y, 0, 1))
Detail solution

  1. Let u=yu = \sqrt{y}.

    Then let du=dy2ydu = \frac{dy}{2 \sqrt{y}} and substitute 2du2 du:

    ∫2 du\int 2\, du

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

      False\text{False}

      1. The integral of a constant is the constant times the variable of integration:

        ∫1 du=u\int 1\, du = u

      So, the result is: 2u2 u

    Now substitute uu back in:

    2y2 \sqrt{y}

  2. Add the constant of integration:

    2y+constant2 \sqrt{y}+ \mathrm{constant}

The answer is:

2y+constant2 \sqrt{y}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                       
 |   1                ___
 | ----- dy = C + 2*\/ y 
 |   ___                 
 | \/ y                  
 |                       
/
∫1y dy=C+2y\int \frac{1}{\sqrt{y}}\, dy = C + 2 \sqrt{y}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900100
Plot the graph f(x)
The answer [src] 
2
22 
=
= 
2
22 
2
Numerical answer [src] 
1.99999999946942
1.99999999946942
The graph
Integral of 1/sqrt(y) dy

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

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