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(1-4x^2)^(1/2)
Solving integrals/ (1-4x^2)^(1/2)

Integral of (1-4x^2)^(1/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
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 |     __________   
 |    /        2    
 |  \/  1 - 4*x   dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \sqrt{1 - 4 x^{2}}\, dx$$ 
Integral(sqrt(1 - 4*x^2), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sin(_theta)/2, rewritten=cos(_theta)**2/2, substep=ConstantTimesRule(constant=1/2, other=cos(_theta)**2, substep=RewriteRule(rewritten=cos(2*_theta)/2 + 1/2, substep=AddRule(substeps=[ConstantTimesRule(constant=1/2, other=cos(2*_theta), substep=URule(u_var=_u, u_func=2*_theta, constant=1/2, substep=ConstantTimesRule(constant=1/2, other=cos(_u), substep=TrigRule(func='cos', arg=_u, context=cos(_u), symbol=_u), context=cos(_u), symbol=_u), context=cos(2*_theta), symbol=_theta), context=cos(2*_theta)/2, symbol=_theta), ConstantRule(constant=1/2, context=1/2, symbol=_theta)], context=cos(2*_theta)/2 + 1/2, symbol=_theta), context=cos(_theta)**2, symbol=_theta), context=cos(_theta)**2/2, symbol=_theta), restriction=(x > -1/2) & (x < 1/2), context=sqrt(1 - 4*x**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                                 
 |                                                                                  
 |    __________          //                 __________                            \
 |   /        2           ||                /        2                             |
 | \/  1 - 4*x   dx = C + | -1/2, x < 1/2)|
/                         \\    4              2                                   /
$$\int \sqrt{1 - 4 x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{1 - 4 x^{2}}}{2} + \frac{\operatorname{asin}{\left(2 x \right)}}{4} & \text{for}\: x > - \frac{1}{2} \wedge x < \frac{1}{2} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              ___
asin(2)   I*\/ 3 
------- + -------
   4         2
$$\frac{\operatorname{asin}{\left(2 \right)}}{4} + \frac{\sqrt{3} i}{2}$$ 
=
= 
              ___
asin(2)   I*\/ 3 
------- + -------
   4         2
$$\frac{\operatorname{asin}{\left(2 \right)}}{4} + \frac{\sqrt{3} i}{2}$$ 
asin(2)/4 + i*sqrt(3)/2
Numerical answer [src] 
(0.392134269538859 + 0.536220266948917j)
(0.392134269538859 + 0.536220266948917j)
The graph
Integral of (1-4x^2)^(1/2) dx

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

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