Mister Exam

Other calculators

Solving integrals/ 2/sqrt(1-xx)

Integral of 2/sqrt(1-xx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

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

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                         
 |                                                          
 |      2                                                   
 | ----------- dx = C + 2*({asin(x)  for And(x > -1, x < 1))
 |   _________                                              
 | \/ 1 - x*x                                               
 |                                                          
/
$$\int \frac{2}{\sqrt{- x x + 1}}\, dx = C + 2 \left(\begin{cases} \operatorname{asin}{\left(x \right)} & \text{for}\: x > -1 \wedge x < 1 \end{cases}\right)$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-pi + 2*asin(2)
$$- \pi + 2 \operatorname{asin}{\left(2 \right)}$$ 
=
= 
-pi + 2*asin(2)
$$- \pi + 2 \operatorname{asin}{\left(2 \right)}$$ 
-pi + 2*asin(2)
Numerical answer [src] 
(0.0 - 2.63391579309942j)
(0.0 - 2.63391579309942j)

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

    © Mister Exam – Calculator