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Find the exact length of the curve.

$ y = 3 + \frac{1}{2} \cosh 2x $ , $ 0 \le x \le 1 $

$l=\frac{e^{2}-e^{-2}}{4}$

Applications of Integration

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Missouri State University

Harvey Mudd College

University of Nottingham

Boston College

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