Integral of 2/sqrtx dx

The solution

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  1         
  /         
 |          
 |    2     
 |  ----- dx
 |    ___   
 |  \/ x    
 |          
/           
0

$$\int\limits_{0}^{1} \frac{2}{\sqrt{x}}\, dx$$

Integral(2/sqrt(x), (x, 0, 1))

Detail solution

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

$\int \frac{2}{\sqrt{x}}\, dx = 2 \int \frac{1}{\sqrt{x}}\, dx$
1. Let $u = \sqrt{x}$ .
  
  Then let $du = \frac{dx}{2 \sqrt{x}}$ 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:
  
  $2 \sqrt{x}$
So, the result is: $4 \sqrt{x}$
Add the constant of integration:

$4 \sqrt{x}+ \mathrm{constant}$

The answer is:

$4 \sqrt{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |   2                ___
 | ----- dx = C + 4*\/ x 
 |   ___                 
 | \/ x                  
 |                       
/

$$\int \frac{2}{\sqrt{x}}\, dx = C + 4 \sqrt{x}$$

Simplify

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Plot the graph f(x)

The answer [src]

$$4$$

Numerical answer [src]

3.99999999893883

3.99999999893883

The graph

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

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Integral of 2/sqrtx dx

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The solution