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(x)/sqrt(four -3x^ two)
(x) divide by square root of (4 minus 3x squared )
(x) divide by square root of (four minus 3x to the power of two)
(x)/√(4-3x^2)
(x)/sqrt(4-3x2)
x/sqrt4-3x2
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x/sqrt4-3x^2
(x) divide by sqrt(4-3x^2)
(x)/sqrt(4-3x^2)dx
Similar expressions
(x)/sqrt(4+3x^2)

Integral of (x)/sqrt(4-3x^2) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |        x         
 |  ------------- dx
 |     __________   
 |    /        2    
 |  \/  4 - 3*x     
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{x}{\sqrt{4 - 3 x^{2}}}\, dx$$

Integral(x/sqrt(4 - 3*x^2), (x, 0, 1))

Detail solution

Let $u = \sqrt{4 - 3 x^{2}}$ .

Then let $du = - \frac{3 x dx}{\sqrt{4 - 3 x^{2}}}$ and substitute $- \frac{du}{3}$ :

$\int \left(- \frac{1}{3}\right)\, du$
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: $- \frac{u}{3}$
Now substitute $u$ back in:

$- \frac{\sqrt{4 - 3 x^{2}}}{3}$
Add the constant of integration:

$- \frac{\sqrt{4 - 3 x^{2}}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{\sqrt{4 - 3 x^{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          __________
 |                          /        2 
 |       x                \/  4 - 3*x  
 | ------------- dx = C - -------------
 |    __________                3      
 |   /        2                        
 | \/  4 - 3*x                         
 |                                     
/

$$\int \frac{x}{\sqrt{4 - 3 x^{2}}}\, dx = C - \frac{\sqrt{4 - 3 x^{2}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3

$$\frac{1}{3}$$

1/3

$$\frac{1}{3}$$

1/3

Numerical answer [src]

0.333333333333333

0.333333333333333

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

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Integral of (x)/sqrt(4-3x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution