Mister Exam

Other calculators

3/√(1-x^2)
Solving integrals/ 3/√(1-x^2)

Integral of 3/√(1-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       3        
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 - x     
 |                
/                 
0
∫0131−x2 dx\int\limits_{0}^{1} \frac{3}{\sqrt{1 - x^{2}}}\, dx 
Integral(3/(sqrt(1 - x^2)), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫31−x2 dx=3∫11−x2 dx\int \frac{3}{\sqrt{1 - x^{2}}}\, dx = 3 \int \frac{1}{\sqrt{1 - x^{2}}}\, dx

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

    So, the result is: 3({asin⁡(x)for x>−1∧x<1)3 \left(\begin{cases} \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right)

  2. Now simplify:

    {3asin⁡(x)for x>−1∧x<1NaNotherwise\begin{cases} 3 \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \\\text{NaN} & \text{otherwise} \end{cases}

  3. Add the constant of integration:

    {3asin⁡(x)for x>−1∧x<1NaNotherwise+constant\begin{cases} 3 \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \\\text{NaN} & \text{otherwise} \end{cases}+ \mathrm{constant}

The answer is:

{3asin⁡(x)for x>−1∧x<1NaNotherwise+constant\begin{cases} 3 \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \\\text{NaN} & \text{otherwise} \end{cases}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                         
 |                                                          
 |      3                                                   
 | ----------- dx = C + 3*({asin(x)  for And(x > -1, x < 1))
 |    ________                                              
 |   /      2                                               
 | \/  1 - x                                                
 |                                                          
/
∫31−x2 dx=C+3({asin⁡(x)for x>−1∧x<1)\int \frac{3}{\sqrt{1 - x^{2}}}\, dx = C + 3 \left(\begin{cases} \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900250
Plot the graph f(x)
The answer [src] 
3*pi
----
 2
3π2\frac{3 \pi}{2} 
=
= 
3*pi
----
 2
3π2\frac{3 \pi}{2}
Упростить
Numerical answer [src] 
4.71238897925936
4.71238897925936
The graph
Integral of 3/√(1-x^2) dx

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

    © Mister Exam – Calculator