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Surface Area of a Revolving Curve

Using the formula for the surface area of a revolving curve about the y-axis:
S=∫2πx√(1 + (dx/dy)²)dy throughout a,b

Find the area of the surface generated by revolving the curve about the y axis within the given boundaries

x=√(2y-1) 5/8≤y≤1

the revolving base passes thru the point (1/2, 5/8)
the revolving top passes thru the point (1,1)

Please be detailed, showing the complete derivation, integration and substitution of limits to find the area.

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S=∫2πx√(1 + ...

Solution Summary

This shows how to use a given formula to find surface area of a revolving curve.