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Identical expressions
x^ two √(one -x^ two)
x squared √(1 minus x squared )
x to the power of two √(one minus x to the power of two)
x2√(1-x2)
x2√1-x2
x²√(1-x²)
x to the power of 2√(1-x to the power of 2)
x^2√1-x^2
x^2√(1-x^2)dx
Similar expressions
x^2√(1+x^2)

Integral of x^2√(1-x^2) dx

The solution

You have entered [src]

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

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

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

The answer (Indefinite) [src]

  /                                                                                     
 |                                                                                      
 |       ________          //               ________                                   \
 |  2   /      2           ||              /      2  /       2\                        |
 | x *\/  1 - x   dx = C + | -1, x < 1)|
/                          \\   8                 8                                    /

$$\int x^{2} \sqrt{1 - x^{2}}\, dx = C + \begin{cases} - \frac{x \left(1 - 2 x^{2}\right) \sqrt{1 - x^{2}}}{8} + \frac{\operatorname{asin}{\left(x \right)}}{8} & \text{for}\: x > -1 \wedge x < 1 \end{cases}$$

Simplify

Numerical answer [src]

0.196349540849362

0.196349540849362

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

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Integral of x^2√(1-x^2) dx

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The solution