1. ## difficult integral

could you help me please to solve this integral

sqrt(1+4sin^(2)(x))

from x=0 to x= pi/2

2. Originally Posted by ameer
could you help me please to solve this integral

sqrt(1+4sin^(2)(x))

from x=0 to x= pi/2
This integral is not expressible in terms of elementary functions.

3. This is an Elliptic Integral:

$\int_{0}^{\frac{\pi}{2}}\sqrt{1+4sin^{2}(x)}dx=\sq rt{5}\text{Elliptic}\left(\frac{2}{\sqrt{5}}\right )$

4. Thank you!