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    Surface Area of a Revolved Curve

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    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.

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    Solution Summary

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