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

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

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                                     
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 |    ________          //     ________                                                \
 |   /      2           ||    /      2        /    ___\                                |
 | \/  2 - x   dx = C + | -\/ 2 , x < \/ 2 /|
/                       \\      2             \   2   /                                /
$$\int \sqrt{2 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{2 - x^{2}}}{2} + \operatorname{asin}{\left(\frac{\sqrt{2} x}{2} \right)} & \text{for}\: x > - \sqrt{2} \wedge x < \sqrt{2} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1   pi
- + --
2   4
$$\frac{1}{2} + \frac{\pi}{4}$$ 
=
= 
1   pi
- + --
2   4
$$\frac{1}{2} + \frac{\pi}{4}$$ 
1/2 + pi/4
Numerical answer [src] 
1.28539816339745
1.28539816339745
The graph
Integral of sqrt(2-x^2) dx

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

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