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Solving integrals/ sqrt(25-x^2)

Integral of sqrt(25-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4                
  /                
 |                 
 |     _________   
 |    /       2    
 |  \/  25 - x   dx
 |                 
/                  
0
$$\int\limits_{0}^{4} \sqrt{25 - x^{2}}\, dx$$ 
Integral(sqrt(25 - x^2), (x, 0, 4))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=5*sin(_theta), rewritten=25*cos(_theta)**2, substep=ConstantTimesRule(constant=25, 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=25*cos(_theta)**2, symbol=_theta), restriction=(x > -5) & (x < 5), context=sqrt(25 - x**2), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                            
 |                                                                             
 |    _________          //       /x\        _________                        \
 |   /       2           ||25*asin|-|       /       2                         |
 | \/  25 - x   dx = C + |<       \5/   x*\/  25 - x                          |
 |                       ||---------- + --------------  for And(x > -5, x < 5)|
/                        \\    2              2                               /
$$\int \sqrt{25 - x^{2}}\, dx = C + \begin{cases} \frac{x \sqrt{25 - x^{2}}}{2} + \frac{25 \operatorname{asin}{\left(\frac{x}{5} \right)}}{2} & \text{for}\: x > -5 \wedge x < 5 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    25*asin(4/5)
6 + ------------
         2
$$6 + \frac{25 \operatorname{asin}{\left(\frac{4}{5} \right)}}{2}$$ 
=
= 
    25*asin(4/5)
6 + ------------
         2
$$6 + \frac{25 \operatorname{asin}{\left(\frac{4}{5} \right)}}{2}$$ 
6 + 25*asin(4/5)/2
Numerical answer [src] 
17.5911902250202
17.5911902250202

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

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