Prove that the integral from 0 to infinity sinx/x =pie/2

Question

anonymous · Answer

$$\int_0^{\infty} \frac{\sin {x}}{x}$$

anonymous · Answer

hmm did you try by parts ??

anonymous · Answer

integration by parts

anonymous · Answer

no. I havent

anonymous · Answer

i am confused about the x in denominator i dunno how to get rid of it

anonymous · Answer

i think it's Si(x) function not sure lemme check

anonymous · Answer

http://www.wolframalpha.com/input/?i=sinx%2Fx+dx+ yeah it is Si(x)

anonymous · Answer

Hmm i dunno about them sorry I won;t be able to help you

anonymous · Answer

this site http://tutorial.math.lamar.edu/Classes/CalcII/IntegrationStrategy.aspx says that the integral can never be solved except with an algebra system

anonymous · Answer

algebra system hmm sounds advanced yet interesting

anonymous · Answer

certainly

anonymous · Answer

can working be shown as to how you can arrive at the answer?

lalaly · Answer

did u take fourier series?

anonymous · Answer

I seriously have no idea on how to do this, i have to study much more to get on something like this

anonymous · Answer

lalaly I didnt
but could u give me insight on that?

zarkon · Answer

you can write it as a double integral and then switch the order of integration...

$$\int\limits_{0}^{\infty}\frac{\sin(x)}{x}dx=\int\limits_{0}^{\infty}\int\limits_{0}^{\infty}e^{-xt}\sin(x)dtdx$$

anonymous · Answer

thanx Ishaan I will await your reply

anonymous · Answer

Zarkon could you please finish it up for me?

zarkon · Answer

I really don't want to ;)...switch the order of integration...then use parts on the first integral...you will end up with a standard inverse trig integral

anonymous · Answer

thanx Zarkon