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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: 1,807

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
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Thanks
PF Gold
P: 39,568

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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