Mister Exam

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Solving integrals/ x/(sqrt(1-(x^2)))

Integral of x/(sqrt(1-(x^2))) dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \sqrt{1 - x^{2}}$ .

Then let $du = - \frac{x dx}{\sqrt{1 - x^{2}}}$ and substitute $- du$ :

$\int \left(-1\right)\, du$
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: $- u$
Now substitute $u$ back in:

$- \sqrt{1 - x^{2}}$
Add the constant of integration:

$- \sqrt{1 - x^{2}}+ \mathrm{constant}$

The answer is:

$- \sqrt{1 - x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                         ________
 |      x                 /      2 
 | ----------- dx = C - \/  1 - x  
 |    ________                     
 |   /      2                      
 | \/  1 - x                       
 |                                 
/

$$\int \frac{x}{\sqrt{1 - x^{2}}}\, dx = C - \sqrt{1 - x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

Numerical answer [src]

0.999999999624892

0.999999999624892

The graph

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

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Integral of x/(sqrt(1-(x^2))) dx

Limits of integration:

The graph:

Piecewise:

The solution