Mister Exam

Other calculators

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

Integral of 1/√(4-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    TrigSubstitutionRule(theta=_theta, func=2*sin(_theta), rewritten=1, substep=ConstantRule(constant=1, context=1, symbol=_theta), restriction=(x > -2) & (x < 2), context=1/(sqrt(4 - x**2)), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                       
 |                                                        
 |      1               //    /x\                        \
 | ----------- dx = C + | -2, x < 2)|
 |    ________          \\    \2/                        /
 |   /      2                                             
 | \/  4 - x                                              
 |                                                        
/
$$\int \frac{1}{\sqrt{4 - x^{2}}}\, dx = C + \begin{cases} \operatorname{asin}{\left(\frac{x}{2} \right)} & \text{for}\: x > -2 \wedge x < 2 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
pi
--
6
$$\frac{\pi}{6}$$ 
=
= 
pi
--
6
$$\frac{\pi}{6}$$ 
pi/6
Numerical answer [src] 
0.523598775598299
0.523598775598299
The graph
Integral of 1/√(4-x^2) dx

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

    © Mister Exam – Calculator