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Integral of 2lnx
Derivative of:
x(4-x^2)^(1/2)
Identical expressions
x(four -x^ two)^(one / two)
x(4 minus x squared ) to the power of (1 divide by 2)
x(four minus x to the power of two) to the power of (one divide by two)
x(4-x2)(1/2)
x4-x21/2
x(4-x²)^(1/2)
x(4-x to the power of 2) to the power of (1/2)
x4-x^2^1/2
x(4-x^2)^(1 divide by 2)
x(4-x^2)^(1/2)dx
Similar expressions
x(4+x^2)^(1/2)

Solving integrals/ x(4-x^2)^(1/2)

Integral of x(4-x^2)^(1/2) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |       ________   
 |      /      2    
 |  x*\/  4 - x   dx
 |                  
/                   
0

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

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

Detail solution

Rewrite the integrand:

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

SqrtQuadraticDenomRule(a=4, b=0, c=-1, coeffs=[-1, 0, 4, 0], context=(-x**3 + 4*x)/sqrt(4 - x**2), symbol=x)
Now simplify:

$- \frac{\left(4 - x^{2}\right)^{\frac{3}{2}}}{3}$
Add the constant of integration:

$- \frac{\left(4 - x^{2}\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{\left(4 - x^{2}\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int x \sqrt{4 - x^{2}}\, dx = C + \sqrt{4 - x^{2}} \left(\frac{x^{2}}{3} - \frac{4}{3}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8     ___
- - \/ 3 
3

$$\frac{8}{3} - \sqrt{3}$$

8     ___
- - \/ 3 
3

$$\frac{8}{3} - \sqrt{3}$$

Упростить

Numerical answer [src]

0.934615859097789

0.934615859097789

The graph

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

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Integral of x(4-x^2)^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution