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sqrt(4x^2-9)
Solving integrals/ sqrt(4x^2-9)

Integral of sqrt(4x^2-9) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     __________   
 |    /    2        
 |  \/  4*x  - 9  dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \sqrt{4 x^{2} - 9}\, dx$$ 
Integral(sqrt(4*x^2 - 9), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                      
 |                               /2*x\        ___________
 |    __________          9*acosh|---|       /         2 
 |   /    2                      \ 3 /   x*\/  -9 + 4*x  
 | \/  4*x  - 9  dx = C - ------------ + ----------------
 |                             4                2        
/
$$\int \sqrt{4 x^{2} - 9}\, dx = C + \frac{x \sqrt{4 x^{2} - 9}}{2} - \frac{9 \operatorname{acosh}{\left(\frac{2 x}{3} \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                     ___         
  9*acosh(2/3)   I*\/ 5    9*pi*I
- ------------ + ------- + ------
       4            2        8
$$- \frac{9 \operatorname{acosh}{\left(\frac{2}{3} \right)}}{4} + \frac{\sqrt{5} i}{2} + \frac{9 i \pi}{8}$$ 
=
= 
                     ___         
  9*acosh(2/3)   I*\/ 5    9*pi*I
- ------------ + ------- + ------
       4            2        8
$$- \frac{9 \operatorname{acosh}{\left(\frac{2}{3} \right)}}{4} + \frac{\sqrt{5} i}{2} + \frac{9 i \pi}{8}$$ 
-9*acosh(2/3)/4 + i*sqrt(5)/2 + 9*pi*i/8
Numerical answer [src] 
(0.0 + 2.75992121526057j)
(0.0 + 2.75992121526057j)
The graph
Integral of sqrt(4x^2-9) dx

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

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