# Determine the length of the curve sin(x)

by Loren Booda
Tags: curve, determine, length, sinx
 Sci Advisor P: 1,794 It's $$\int^{2\pi}_0\sqrt{\cos(x)^2+1} dx$$
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,502 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 $$\int_{x=a}^b \sqrt{1+ f'(x)^2}dx$$ With y= f(x)= sin(x), f'(x)= cos(x) so that becomes $$\int_{x=0}^{2\pi} \sqrt{1+ cos^2(x)}dx$$ 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!