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1/sqrt(9-x^2)
Solving integrals/ 1/sqrt(9-x^2)

Integral of 1/sqrt(9-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  9 - x     
 |                
/                 
0
$$\int\limits_{0}^{3} \frac{1}{\sqrt{9 - x^{2}}}\, dx$$ 
Integral(1/(sqrt(9 - x^2)), (x, 0, 3))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=3*sin(_theta), rewritten=1, substep=ConstantRule(constant=1, context=1, symbol=_theta), restriction=(x > -3) & (x < 3), context=1/(sqrt(9 - x**2)), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                       
 |                                                        
 |      1               //    /x\                        \
 | ----------- dx = C + | -3, x < 3)|
 |    ________          \\    \3/                        /
 |   /      2                                             
 | \/  9 - x                                              
 |                                                        
/
$$\int \frac{1}{\sqrt{9 - x^{2}}}\, dx = C + \begin{cases} \operatorname{asin}{\left(\frac{x}{3} \right)} & \text{for}\: x > -3 \wedge x < 3 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
pi
--
2
$$\frac{\pi}{2}$$ 
=
= 
pi
--
2
$$\frac{\pi}{2}$$ 
pi/2
Numerical answer [src] 
1.5707963264197
1.5707963264197
The graph
Integral of 1/sqrt(9-x^2) dx

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

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