Question

Compute the surface area of the surface generated by revolving one arch of the cycloid c(t)=(10t−10sint,10−10cost) about the x-axis. Hint: Use the trigonometric identity: 1−cost=2sin^2(t^2).

Answer 1

consider a plane curve \(\gamma\) parameterized as \(r:[a,b]\to\mathbb{R}^2\)