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sqrt(4-y^2)
Solving integrals/ sqrt(4-y^2)

Integral of sqrt(4-y^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     ________   
 |    /      2    
 |  \/  4 - y   dy
 |                
/                 
0
$$\int\limits_{0}^{1} \sqrt{4 - y^{2}}\, dy$$ 
Integral(sqrt(4 - y^2), (y, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=2*sin(_theta), rewritten=4*cos(_theta)**2, substep=ConstantTimesRule(constant=4, 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=4*cos(_theta)**2, symbol=_theta), restriction=(y > -2) & (y < 2), context=sqrt(4 - y**2), symbol=y)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                         
 |                                                                          
 |    ________          //                 ________                        \
 |   /      2           ||                /      2                         |
 | \/  4 - y   dy = C + |<      /y\   y*\/  4 - y                          |
 |                      ||2*asin|-| + -------------  for And(y > -2, y < 2)|
/                       \\      \2/         2                              /
$$\int \sqrt{4 - y^{2}}\, dy = C + \begin{cases} \frac{y \sqrt{4 - y^{2}}}{2} + 2 \operatorname{asin}{\left(\frac{y}{2} \right)} & \text{for}\: y > -2 \wedge y < 2 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___     
\/ 3    pi
----- + --
  2     3
$$\frac{\sqrt{3}}{2} + \frac{\pi}{3}$$ 
=
= 
  ___     
\/ 3    pi
----- + --
  2     3
$$\frac{\sqrt{3}}{2} + \frac{\pi}{3}$$ 
sqrt(3)/2 + pi/3
Numerical answer [src] 
1.91322295498104
1.91322295498104
The graph
Integral of sqrt(4-y^2) dx

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

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