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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    SqrtQuadraticRule(a=9, b=0, c=-1, context=sqrt(9 - x**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                              
 |                            /x\        ________
 |    ________          9*asin|-|       /      2 
 |   /      2                 \3/   x*\/  9 - x  
 | \/  9 - x   dx = C + --------- + -------------
 |                          2             2      
/
$${{x\,\sqrt{9-x^2}}\over{2}}+{{9\,\arcsin \left({{x}\over{3}}\right) }\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___   9*asin(1/3)
\/ 2  + -----------
             2
$${{9\,\arcsin \left({{1}\over{3}}\right)+2^{{{3}\over{2}}}}\over{2}}$$ 
=
= 
  ___   9*asin(1/3)
\/ 2  + -----------
             2
$$\sqrt{2} + \frac{9 \operatorname{asin}{\left(\frac{1}{3} \right)}}{2}$$
Simplify
Numerical answer [src] 
2.94347965491664
2.94347965491664
The graph
Integral of (9-x^2)^(1/2) dx

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

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