Integration of sqrt(sinx)

Question

lgbasallote · Answer

interesting...

$$\int \sqrt{\sin x}dx$$
right?

anonymous · Answer

Yeah!

anonymous · Answer

@lgbasallote Can you plz give me the solution. Completely raked my brains and still no solution!!!

lgbasallote · Answer

lol i dont wanna hurt mine =)))

anonymous · Answer

Yeah right!!!!!!!!

anonymous · Answer

@experimentX  Can you plz give me the solution. Completely raked my brains and still no solution!!!

experimentx · Answer

One was is
$$ \sqrt{\sin x} = {1 \over 2i}(e^{ix}-e^{-ix})$$

anonymous · Answer

@experimentX Can you tell me how to get the answer. I am interested in the process by which you solved.

experimentx · Answer

oh, that follows from the definition
$$ e^{ix} = \cos x + i\sin x$$

terenzreignz · Answer

Try Integration by parts, perhaps?

anonymous · Answer

@experimentX can you please elaborate.

experimentx · Answer

do you know that Euler's identity?

anonymous · Answer

No i dont know.

experimentx · Answer

sorry .. that wouldn't work. I didn't realize it does not have any closed form http://www.wolframalpha.com/input/?i=integrate+sqrt%28sin+x%29

anonymous · Answer

What the heck is this? http://reference.wolfram.com/mathematica/ref/EllipticE.html

experimentx · Answer

elliptic integrals are non elementary integrals associated with arc length of ellipse. I don't know much about it.

anonymous · Answer

@mukushla 

$$\int\limits \sqrt{\sin (\tan^{-1}{2t})}  \ \ dx$$

dx turns into dt here how exactly?  o_O

anonymous · Answer

is the integral solvable??

anonymous · Answer

@.Sam. HELP!!

experimentx · Answer

wolfram says it is not.

.sam. · Answer

I'm just guessing
$$\int\limits_{}^{}\sqrt{sinx}~dx$$
$$\int\limits\limits_{}^{}\sin(x)^\frac{1}{2}~dx$$
$$-\frac{2\sin(x)^\frac{3}{2}}{3\cos(x)}$$
But you can't use this because this integral is not elementary. So, you have to reduce it to an elliptic integral like what they said.