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sqrt(x^2-1)
Solving integrals/ sqrt(x^2-1)

Integral of sqrt(x^2-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1/2              
   /               
  |                
  |     ________   
  |    /  2        
  |  \/  x  - 1  dx
  |                
 /                 
-1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \sqrt{x^{2} - 1}\, dx$$ 
Integral(sqrt(x^2 - 1), (x, -1/2, 1/2))
The answer (Indefinite) [src] 
  /                                              
 |                                      _________
 |    ________                         /       2 
 |   /  2               acosh(x)   x*\/  -1 + x  
 | \/  x  - 1  dx = C - -------- + --------------
 |                         2             2       
/
$$\int \sqrt{x^{2} - 1}\, dx = C + \frac{x \sqrt{x^{2} - 1}}{2} - \frac{\operatorname{acosh}{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    ___       
I*\/ 3    pi*I
------- + ----
   4       6
$$\frac{\sqrt{3} i}{4} + \frac{i \pi}{6}$$ 
=
= 
    ___       
I*\/ 3    pi*I
------- + ----
   4       6
$$\frac{\sqrt{3} i}{4} + \frac{i \pi}{6}$$ 
i*sqrt(3)/4 + pi*i/6
Numerical answer [src] 
(0.0 + 0.956611477490518j)
(0.0 + 0.956611477490518j)
The graph
Integral of sqrt(x^2-1) dx

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

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