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Problem 16 Easy Difficulty
Find the exact length of the curve.
$ y = 3 + \frac{1}{2} \cosh 2x $ , $ 0 \le x \le 1 $
Answer
$l=\frac{e^{2}-e^{-2}}{4}$
Topics
Applications of Integration
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Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Kayleah T.
Harvey Mudd College
Samuel H.
University of Nottingham
Joseph L.
Boston College
Watch More Solved Questions in Chapter 8
Video Transcript
ants Claressa when you raid here. So we're gonna find the curve length of the curve. So we get the Y over DX to be signed two x, and we're going to square both sides and add one to the expression. So when we do that, we get one plus d y over tea cups square, it goes one plus square two x is equal to And when we recall the identity the hyperbolic sign and coast on eternity we get gosh square of two months. Don't we square? Root the expression? No. We're gonna integrate from 0 to 1. Caution two X t x. This becomes equal to one. Have a sign. I probably like function of two x from 0 to 1. This is equal to e square minus eat the negative two over for
Topics
Applications of Integration
Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Kayleah T.
Harvey Mudd College
Samuel H.
University of Nottingham
Joseph L.
Boston College
