# How do you find the area of the surface generated by rotating the curve about the y-axis #x=t^2, y=1/3t^3, 0<=t<=3#?

##### 1 Answer

Jul 30, 2018

For infinitesimal arc length,

# {(x = t^2, dx = 2 t\ dt),(y = 1/3 t^3, dy = t^2\ dt):}#

Spinning round the y-axis, creating infinitesimal surface area

#dS = 2 pi \ x \ ds#

I have skipped the mechanical integration steps. you can start with a sub:

#u = 4 + t^2 qquad du = 2 t \ dt#

Which is trivial but protracted