# What is the arc length of the curve given by f ( x ) = 1 + cos &#x2061;<!-- ⁡ -->

What is the arc length of the curve given by $f\left(x\right)=1+\mathrm{cos}x$ in the interval $x\in \left[0,2\pi \right]$?
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Tristin Case
Recall that arc length is given by $A={\int }_{a}^{b}\sqrt{1+\left(\frac{dy}{dx}{\right)}^{2}}dx$
The derivative of f'(x) is ${f}^{\prime }\left(x\right)=-\mathrm{sin}x$
$A={\int }_{0}^{2\pi }\sqrt{1+\left(-\mathrm{sin}x{\right)}^{2}}dx$
$A={\int }_{0}^{2\pi }\sqrt{1+{\mathrm{sin}}^{2}x}$
An approximation using a calculator gives A=7.64