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Solving integrals/ 4x/sqrt1-x²

Integral of 4x/sqrt1-x² dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___               
 \/ 3                
   /                 
  |                  
  |   / 4*x     2\   
  |   |----- - x | dx
  |   |  ___     |   
  |   \\/ 1      /   
  |                  
 /                   
  ___                
\/ 3                 
-----                
  3
$$\int\limits_{\frac{\sqrt{3}}{3}}^{\sqrt{3}} \left(- x^{2} + \frac{4 x}{\sqrt{1}}\right)\, dx$$ 
Integral((4*x)/sqrt(1) - x^2, (x, sqrt(3)/3, sqrt(3)))
Detail solution

  1. Integrate term-by-term:

    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:

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

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                               
 |                               3
 | / 4*x     2\             2   x 
 | |----- - x | dx = C + 2*x  - --
 | |  ___     |                 3 
 | \\/ 1      /                   
 |                                
/
$$\int \left(- x^{2} + \frac{4 x}{\sqrt{1}}\right)\, dx = C - \frac{x^{3}}{3} + 2 x^{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          ___
16   26*\/ 3 
-- - --------
3       27
$$\frac{16}{3} - \frac{26 \sqrt{3}}{27}$$ 
=
= 
          ___
16   26*\/ 3 
-- - --------
3       27
$$\frac{16}{3} - \frac{26 \sqrt{3}}{27}$$ 
16/3 - 26*sqrt(3)/27
Numerical answer [src] 
3.66543255567441
3.66543255567441

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

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