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xsqrt(3-x^2)

Integral of xsqrt(3-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |       ________   
 |      /      2    
 |  x*\/  3 - x   dx
 |                  
/                   
0                   
$$\int\limits_{0}^{1} x \sqrt{3 - x^{2}}\, dx$$
Integral(x*sqrt(3 - x^2), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                  
 |                                3/2
 |      ________          /     2\   
 |     /      2           \3 - x /   
 | x*\/  3 - x   dx = C - -----------
 |                             3     
/                                    
$$\int x \sqrt{3 - x^{2}}\, dx = C - \frac{\left(3 - x^{2}\right)^{\frac{3}{2}}}{3}$$
The graph
The answer [src]
            ___
  ___   2*\/ 2 
\/ 3  - -------
           3   
$$- \frac{2 \sqrt{2}}{3} + \sqrt{3}$$
=
=
            ___
  ___   2*\/ 2 
\/ 3  - -------
           3   
$$- \frac{2 \sqrt{2}}{3} + \sqrt{3}$$
sqrt(3) - 2*sqrt(2)/3
Numerical answer [src]
0.789241765986814
0.789241765986814
The graph
Integral of xsqrt(3-x^2) dx

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