## Problem Statement

Calculate the lengths of the arcs of the curves given by equations in a rectangular coordinate system.

$$
y=\frac{e^{x}+e^{-x}}{2}+3, \quad 0 \leq x \leq 2
$$
## Solution

$$
l=\int_{0}^{2} \sqrt{1+\left(\frac{e^{x}-e^{-x}}{2}\right)^{2}} d x=\int_{0}^{2} \sqrt{\frac{4 e^{2 x}+e^{4 x}-2 e^{2 x}+1}{4 e^{2 x}}} d x=\int_{0}^{2} \frac{e^{2 x}+1}{2 e^{x}}=\left.\frac{1}{2}\left(e^{x}-e^{-x}\right)\right|_{0} ^{2}=\frac{1}{2}\left(e^{2}-e^{-2}\right)
$$

Source — "http://pluspi.org/wiki/index.php/?%?%?%?%?%?%?%?%?%?%? \%D0\%9A\%D1\%83\%D0\%B7 \%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD\%D1\%82\%D0\%B5\%D0\%B3\%D1\%80\%D0\%B0\%D0\%BB $\%$ D1\%8B_17-27"

Categories: Kuznetsov Integral Problems 17 | Integrals

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## Problem Kuznetsov Integrals 17-28

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