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Identical expressions
pi(six /x)^ two
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pi(6/x)2
pi6/x2
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pi(6/x) to the power of 2
pi6/x^2
pi(6 divide by x)^2
pi(6/x)^2dx

Solving integrals/ pi(6/x)^2

Integral of pi(6/x)^2 dx

The solution

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  4           
  /           
 |            
 |        2   
 |     /6\    
 |  pi*|-|  dx
 |     \x/    
 |            
/             
1

$$\int\limits_{1}^{4} \pi \left(\frac{6}{x}\right)^{2}\, dx$$

Integral(pi*(6/x)^2, (x, 1, 4))

Detail solution

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

$\int \pi \left(\frac{6}{x}\right)^{2}\, dx = \pi \int \left(\frac{6}{x}\right)^{2}\, dx$
1. Let $u = \frac{6}{x}$ .
  
  Then let $du = - \frac{6 dx}{x^{2}}$ and substitute $- 6 du$ :
  
  $\int 36\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(-6\right)\, du = - 6 \int 1\, du$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $- 6 u$
  Now substitute $u$ back in:
  
  $- \frac{36}{x}$
So, the result is: $- \frac{36 \pi}{x}$
Add the constant of integration:

$- \frac{36 \pi}{x}+ \mathrm{constant}$

The answer is:

$- \frac{36 \pi}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |       2               
 |    /6\           36*pi
 | pi*|-|  dx = C - -----
 |    \x/             x  
 |                       
/

$$-{{36\,\pi}\over{x}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

27*pi

$$27\,\pi$$

27*pi

$$27 \pi$$

Упростить

Numerical answer [src]

84.8230016469244

84.8230016469244

The graph

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

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Identical expressions

Integral of pi(6/x)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution