Utilise the following formula that gives the surface area of a curve that revolves around the y-axis:
S=∫2πx√(1 + (dx/dy)²)dy throughout c, d
Now calculate the area of the surface that would come about by rotating the curve around the y axis with the boundaries below:
x = (1/3)y³′² - y ¹′² 1≤y≤3
Aim to be detailed - give the complete derivation, integration and substitution of limits to calculate the area.
Thsi shows how to find the surface area of a solid of revolution.