October 5th, 2018, 05:49 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 588 Thanks: 86  Definite Integral
Post different ways and methods for solution of the integral $\displaystyle \int \limits_0^{1} \frac{\sin x}{x} dx $

October 5th, 2018, 06:08 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 
There is no familiar closed form for this. $\displaystyle \int_0^x~\dfrac{\sin(z)}{z}~dz = Si(x)$ where $Si(x)$ is known as the sine integral function 
October 5th, 2018, 07:14 PM  #3  
Senior Member Joined: Oct 2016 From: Arizona Posts: 209 Thanks: 37 Math Focus: I'm still deciding, but my recent focus has been olympiad problems and math journal problems.  Quote:
 

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