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√(9-x^2)

Integral of √(9-x^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    
 |  \/  9 - x   dx
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/                 
0                 
$$\int\limits_{0}^{1} \sqrt{9 - x^{2}}\, dx$$
Integral(sqrt(9 - x^2), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                         
 |                                                                          
 |    ________          //      /x\        ________                        \
 |   /      2           ||9*asin|-|       /      2                         |
 | \/  9 - x   dx = C + |<      \3/   x*\/  9 - x                          |
 |                      ||--------- + -------------  for And(x > -3, x < 3)|
/                       \\    2             2                              /
$$\int \sqrt{9 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{9 - x^{2}}}{2} + \frac{9 \operatorname{asin}{\left(\frac{x}{3} \right)}}{2} & \text{for}\: x > -3 \wedge x < 3 \end{cases}$$
The graph
The answer [src]
  ___   9*asin(1/3)
\/ 2  + -----------
             2     
$$\sqrt{2} + \frac{9 \operatorname{asin}{\left(\frac{1}{3} \right)}}{2}$$
=
=
  ___   9*asin(1/3)
\/ 2  + -----------
             2     
$$\sqrt{2} + \frac{9 \operatorname{asin}{\left(\frac{1}{3} \right)}}{2}$$
sqrt(2) + 9*asin(1/3)/2
Numerical answer [src]
2.94347965491664
2.94347965491664
The graph
Integral of √(9-x^2) dx

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