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sqrt(1-r^2)*r

Integral of sqrt(1-r^2)*r dr

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |     ________     
 |    /      2      
 |  \/  1 - r  *r dr
 |                  
/                   
0                   
$$\int\limits_{0}^{1} r \sqrt{1 - r^{2}}\, dr$$
Integral(sqrt(1 - r^2)*r, (r, 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             \1 - r /   
 | \/  1 - r  *r dr = C - -----------
 |                             3     
/                                    
$$\int r \sqrt{1 - r^{2}}\, dr = C - \frac{\left(1 - r^{2}\right)^{\frac{3}{2}}}{3}$$
The graph
The answer [src]
1/3
$$\frac{1}{3}$$
=
=
1/3
$$\frac{1}{3}$$
1/3
Numerical answer [src]
0.333333333333333
0.333333333333333
The graph
Integral of sqrt(1-r^2)*r dr

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