What is the arc length of the curve given by $f(x)=1+\mathrm{cos}x$ in the interval $x\in [0,2\pi ]$?

Keenan Santos
2022-07-12
Answered

What is the arc length of the curve given by $f(x)=1+\mathrm{cos}x$ in the interval $x\in [0,2\pi ]$?

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Tristin Case

Answered 2022-07-13
Author has **15** answers

Recall that arc length is given by $A={\int}_{a}^{b}\sqrt{1+(\frac{dy}{dx}{)}^{2}}dx$

The derivative of f'(x) is ${f}^{\prime}(x)=-\mathrm{sin}x$

$A={\int}_{0}^{2\pi}\sqrt{1+(-\mathrm{sin}x{)}^{2}}dx$

$A={\int}_{0}^{2\pi}\sqrt{1+{\mathrm{sin}}^{2}x}$

An approximation using a calculator gives A=7.64

The derivative of f'(x) is ${f}^{\prime}(x)=-\mathrm{sin}x$

$A={\int}_{0}^{2\pi}\sqrt{1+(-\mathrm{sin}x{)}^{2}}dx$

$A={\int}_{0}^{2\pi}\sqrt{1+{\mathrm{sin}}^{2}x}$

An approximation using a calculator gives A=7.64

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