Calculate the surface area of the surface obtained when the region enclosed by the given curves is revolved about the $x$-axis $$y=2x^2-8$$ $$y=x^2-1$$
This is a model problem for an exam and I really don't know what to do. I don't have any idea what shape will I get when the given curves are revolved around the x-axis. Can somebody help me with this problem?
Can I consider these areas for the calculation
I won't do the whole problem but the $3$ surfaces are on the intervals $[0, 1.7320508],$
$[1.7320508, 2.6457513]\ \text{and} \ [2, 2.6457513]$ whereby symmetry about the y axis means doubling each area to get the total area.