October 5th, 2018, 05:49 AM  #1 
Senior Member Joined: Dec 2015 From: Earth Posts: 248 Thanks: 27  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: 2,122 Thanks: 1102 
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: 127 Thanks: 27 Math Focus: Frame Theory is pretty awesome, and it's ripe for undergraduate research!  Quote:
 

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