Mister Exam

Other calculators

sqrt(16-x^2)
Solving integrals/ sqrt(16-x^2)

Integral of sqrt(16-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4                
  /                
 |                 
 |     _________   
 |    /       2    
 |  \/  16 - x   dx
 |                 
/                  
-4
$$\int\limits_{-4}^{4} \sqrt{16 - x^{2}}\, dx$$ 
Integral(sqrt(16 - x^2), (x, -4, 4))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=4*sin(_theta), rewritten=16*cos(_theta)**2, substep=ConstantTimesRule(constant=16, 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=16*cos(_theta)**2, symbol=_theta), restriction=(x > -4) & (x < 4), context=sqrt(16 - x**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                           
 |                                                                            
 |    _________          //                 _________                        \
 |   /       2           ||                /       2                         |
 | \/  16 - x   dx = C + |<      /x\   x*\/  16 - x                          |
 |                       ||8*asin|-| + --------------  for And(x > -4, x < 4)|
/                        \\      \4/         2                               /
$$\int \sqrt{16 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{16 - x^{2}}}{2} + 8 \operatorname{asin}{\left(\frac{x}{4} \right)} & \text{for}\: x > -4 \wedge x < 4 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
8*pi
$$8 \pi$$ 
=
= 
8*pi
$$8 \pi$$ 
8*pi
Numerical answer [src] 
25.1327412287183
25.1327412287183
The graph
Integral of sqrt(16-x^2) dx

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

    © Mister Exam – Calculator