Question

Find the area of the surface obtained by rotating the given curve about the x-axis
x=3t-t^3, y=3t^2, 0≤t≤1

Please help me with this problem.

Answer 1

The formula for the surface area of a shape revolved around the x-axis in parametric coordinates, is:\[SA \ = \ 2 \pi *\int\limits_{a}^{b} \ \ y \ * \sqrt{(dy/dt)^2+(dx/dt)^2.} \ dt\] Apply to your problem, and presto. :)