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dx/sqrt(4-25x^2)
Solving integrals/ dx/sqrt(4-25x^2)

Integral of dx/sqrt(4-25x^2) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |       ___________   
 |      /         2    
 |    \/  4 - 25*x     
 |                     
/                      
0
∫011⋅1−25x2+4 dx\int\limits_{0}^{1} 1 \cdot \frac{1}{\sqrt{- 25 x^{2} + 4}}\, dx
Simplify
Detail solution

    TrigSubstitutionRule(theta=_theta, func=2*sin(_theta)/5, rewritten=1/5, substep=ConstantRule(constant=1/5, context=1/5, symbol=_theta), restriction=(x > -2/5) & (x < 2/5), context=1/sqrt(4 - 25*x**2), symbol=x)

  1. Now simplify:

    {asin⁡(5x2)5for x>−25∧x<25NaNotherwise\begin{cases} \frac{\operatorname{asin}{\left(\frac{5 x}{2} \right)}}{5} & \text{for}\: x > - \frac{2}{5} \wedge x < \frac{2}{5} \\\text{NaN} & \text{otherwise} \end{cases}

  2. Add the constant of integration:

    {asin⁡(5x2)5for x>−25∧x<25NaNotherwise+constant\begin{cases} \frac{\operatorname{asin}{\left(\frac{5 x}{2} \right)}}{5} & \text{for}\: x > - \frac{2}{5} \wedge x < \frac{2}{5} \\\text{NaN} & \text{otherwise} \end{cases}+ \mathrm{constant}

The answer is:

{asin⁡(5x2)5for x>−25∧x<25NaNotherwise+constant\begin{cases} \frac{\operatorname{asin}{\left(\frac{5 x}{2} \right)}}{5} & \text{for}\: x > - \frac{2}{5} \wedge x < \frac{2}{5} \\\text{NaN} & \text{otherwise} \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                  
 |                           //    /5*x\                            \
 |         1                 ||asin|---|                            |
 | 1*-------------- dx = C + |<    \ 2 /                            |
 |      ___________          ||---------  for And(x > -2/5, x < 2/5)|
 |     /         2           \\    5                                /
 |   \/  4 - 25*x                                                    
 |                                                                   
/
arcsin⁡(5 x2)5{{\arcsin \left({{5\,x}\over{2}}\right)}\over{5}}
Simplify
The graph
0.000.050.100.150.200.250.300.350.40050
Plot the graph f(x)
The answer [src] 
asin(5/2)
---------
    5
arcsin⁡(52)5{{\arcsin \left({{5}\over{2}}\right)}\over{5}} 
=
= 
asin(5/2)
---------
    5
asin⁡(52)5\frac{\operatorname{asin}{\left(\frac{5}{2} \right)}}{5}
Simplify
Numerical answer [src] 
(0.286954509007177 - 0.320835134585762j)
(0.286954509007177 - 0.320835134585762j)
The graph
Integral of dx/sqrt(4-25x^2) dx

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

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