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Solving integrals/ sqrt(1+4y^2)

Integral of sqrt(1+4y^2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  1 + 4*y   dy
 |                  
/                   
0
$$\int\limits_{0}^{2} \sqrt{4 y^{2} + 1}\, dy$$ 
Integral(sqrt(1 + 4*y^2), (y, 0, 2))
The answer (Indefinite) [src] 
  /                                                   
 |                                          __________
 |    __________                           /        2 
 |   /        2           asinh(2*y)   y*\/  1 + 4*y  
 | \/  1 + 4*y   dy = C + ---------- + ---------------
 |                            4               2       
/
$$\int \sqrt{4 y^{2} + 1}\, dy = C + \frac{y \sqrt{4 y^{2} + 1}}{2} + \frac{\operatorname{asinh}{\left(2 y \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ____   asinh(4)
\/ 17  + --------
            4
$$\frac{\operatorname{asinh}{\left(4 \right)}}{4} + \sqrt{17}$$ 
=
= 
  ____   asinh(4)
\/ 17  + --------
            4
$$\frac{\operatorname{asinh}{\left(4 \right)}}{4} + \sqrt{17}$$ 
sqrt(17) + asinh(4)/4
Numerical answer [src] 
4.64678376243294
4.64678376243294

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

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