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Determine the length of the curve sin(x) 
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#1
Mar2112, 06:51 PM

P: 3,408

What is the measure of the sin(x) wave for x=0 to 2∏?



#2
Mar2112, 06:56 PM

Sci Advisor
P: 1,742

It's [tex]\int^{2\pi}_0\sqrt{\cos(x)^2+1} dx[/tex]



#3
Mar2112, 07:13 PM

P: 3,408

That's what I got. Would one need a table of integrals to determine its numerical value?



#4
Mar2112, 07:13 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,361

Determine the length of the curve sin(x)
Pretty straight forward, isn't it? Considering the other problems you have posted on here, you should be able to do this.
The length of the graph of y= f(x), from x= a to x= b, is given by [tex]\int_{x=a}^b \sqrt{1+ f'(x)^2}dx[/tex] With y= f(x)= sin(x), f'(x)= cos(x) so that becomes [tex]\int_{x=0}^{2\pi} \sqrt{1+ cos^2(x)}dx[/tex] However, that looks to me like a version of an elliptical integral which cannot be done in terms of elementary functions. Hey, no fair posting while I'm typing! 


#5
Mar2112, 07:18 PM

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P: 15,067




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