Specialist2026 NHT Exam 2 Section A · Q10CAS active1 mark

Surface area of a parametric curve rotated about the x-axis

The curve defined by the parametric equations $x = 2t - \sin(2t)$ , $y = 1 - \cos(2t)$ for $0 \le t \le \pi$ is rotated about the $x$ -axis to form a surface of revolution.

The area of this surface is given by

1 mark

16\pi\displaystyle\int_0^{\pi} \cos^3(t)\,dt

16\pi\displaystyle\int_0^{\pi} \sin^3(t)\,dt

64\pi\displaystyle\int_0^{\pi} \sin^4(t)\,dt

64\pi\displaystyle\int_0^{\pi} \cos^4(t)\,dt

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