Mister Exam

Other calculators

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                       
 |                                                                        
 |    ________          //               ________                        \
 |   /      2           ||              /      2                         |
 | \/  1 - x   dx = C + | -1, x < 1)|
/                       \\   2            2                              /
$$\int \sqrt{1 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{1 - x^{2}}}{2} + \frac{\operatorname{asin}{\left(x \right)}}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
pi
--
4
$$\frac{\pi}{4}$$ 
=
= 
pi
--
4
$$\frac{\pi}{4}$$ 
pi/4
Numerical answer [src] 
0.785398163397448
0.785398163397448
The graph
Integral of sqrt(1-x^2)dx dx

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

    © Mister Exam – Calculator