How to find length of curve
Favorites|Homepage
Subscriptions | sitemap
HOME > > How to find length of curve

How to find length of curve

[From: ] [author: ] [Date: 12-10-17] [Hit: ]
∫ cosh2x dx -------cosh²2x - sinh²2x = 1,= 1/2 sinh2x,......
Find the exact length of the curve:
y=3+(1/2)cosh(2x) 0<=x<=1

Cannot figure out this problem. Is y'=sinh(2x)?
If it is I have L=integral from 0 to 1 of (sqrt(1+(sinh(2x))^2)). Don't know where to go from here if I even did it right. I've never worked with cosh before. Help would be great. Thanks!

-
You are right on!
1
∫ √[(dx)² + (dy) ²]
0
1
∫ √[1 + (y)' ²] dx
0
1
∫ √[1 + sinh²2x] dx
0
1
∫ cosh2x dx ------- cosh²2x - sinh²2x = 1, cosh2x is always positive
0
= 1/2 sinh2x, x from 0 to 1
=1/2 sinh2
=(e⁴ - 1)/(4e²)
1
keywords: curve,to,How,length,find,of,How to find length of curve
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .