Answer the following True or False:
If the arc length ∫αβr2+(drdθ)2dθ=∫αβrdθ,0≤α<β≤2π\displaystyle {\int_{\alpha}^{\beta}}\sqrt{{{r}^{{2}}+{\left(\frac{{{d}{r}}}{{{d}\theta}}\right)}^{{2}}}}{d}\theta={\int_{\alpha}^{\beta}}{r}{d}\theta,{0}\le\alpha<\beta\le{2}\pi∫αβr2+(dθdr)2dθ=∫αβrdθ,0≤α<β≤2π then the curve r=r(θ)\displaystyle {r}={r}{\left(\theta\right)}r=r(θ) is an arc of a circle.
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