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Surface Area of a Revolved Curve

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.

Solution Summary

Thsi shows how to find the surface area of a solid of revolution.