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Solving integrals/ 4/sqrt(x)

Integral of 4/sqrt(x) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
 25         
  /         
 |          
 |    4     
 |  ----- dx
 |    ___   
 |  \/ x    
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/           
9
∫9254x dx\int\limits_{9}^{25} \frac{4}{\sqrt{x}}\, dx 
Integral(4/sqrt(x), (x, 9, 25))
Detail solution

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

    ∫4x dx=4∫1x dx\int \frac{4}{\sqrt{x}}\, dx = 4 \int \frac{1}{\sqrt{x}}\, dx

    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}

    So, the result is: 8x8 \sqrt{x}

  2. Add the constant of integration:

    8x+constant8 \sqrt{x}+ \mathrm{constant}

The answer is:

8x+constant8 \sqrt{x}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                       
 |   4                ___
 | ----- dx = C + 8*\/ x 
 |   ___                 
 | \/ x                  
 |                       
/
∫4x dx=C+8x\int \frac{4}{\sqrt{x}}\, dx = C + 8 \sqrt{x}
Simplify
The graph
1012141618202224050
Plot the graph f(x)
The answer [src] 
16
1616 
=
= 
16
1616 
16
Numerical answer [src] 
16.0
16.0

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

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