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1/√x
Solving integrals/ 1/√x

Integral of 1/√x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let u=xu = \sqrt{x}.

    Then let du=dx2xdu = \frac{dx}{2 \sqrt{x}} 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:

    2x2 \sqrt{x}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                      
 |                       
 |   1                ___
 | ----- dx = C + 2*\/ x 
 |   ___                 
 | \/ x                  
 |                       
/
∫1x dx=C+2x\int \frac{1}{\sqrt{x}}\, dx = C + 2 \sqrt{x}
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/√x dx

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

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