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x√ four -x^ two
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Similar expressions
x√4+x^2

Solving integrals/ x√4-x^2

Integral of x√4-x^2 dx

The solution

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  0                  
  /                  
 |                   
 |  /    ___    2\   
 |  \x*\/ 4  - x / dx
 |                   
/                    
-2

$$\int\limits_{-2}^{0} \left(- x^{2} + \sqrt{4} x\right)\, dx$$

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sqrt{4} x\, dx = 2 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $x^{2}$
The result is: $- \frac{x^{3}}{3} + x^{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-20/3

$$- \frac{20}{3}$$

-20/3

$$- \frac{20}{3}$$

Упростить

Numerical answer [src]

-6.66666666666667

-6.66666666666667

The graph

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

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Integral of x√4-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution