Specialist2024 Exam 2 Section A · Q9CAS active1 mark

Arc length of a parametric curve

The length of the curve specified by $x = 1 - \cos(t)$ and $y = t - \sin(t)$ , where $t \in [0, 2\pi]$ , is given by

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\displaystyle\int_0^{2\pi} 2\sin\left(\frac{t}{2}\right) dt

\displaystyle\int_0^{2\pi} \sqrt{(1-\cos(t))^2 + (t-\sin(t))^2}\, dt

\displaystyle 2\int_0^{2\pi} (1-\cos(t))\, dt

\displaystyle\int_0^{2\pi} 2\cos\left(\frac{t}{2}\right) dt

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